11 Search Results for "Eleftheriadis, Ioannis"

Document
DOI: 10.4230/LIPIcs.CSL.2026.41
Weakly-Sparse and Strongly Flip-Flat Classes of Graphs Are Uniformly Almost-Wide

Authors: Fatemeh Ghasemi, Julien Grange, Mamadou Moustapha Kanté, and Florent Madelaine

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
In this work we take a step towards characterising strongly flip-flat classes of graphs. Strong flip-flatness appears to be the analogue of uniform almost-wideness in the setting of dense classes of graphs. We prove that strongly flip-flat classes of graphs that are weakly sparse are indeed uniformly almost-wide.
Cite as

Fatemeh Ghasemi, Julien Grange, Mamadou Moustapha Kanté, and Florent Madelaine. Weakly-Sparse and Strongly Flip-Flat Classes of Graphs Are Uniformly Almost-Wide. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghasemi_et_al:LIPIcs.CSL.2026.41,
  author =	{Ghasemi, Fatemeh and Grange, Julien and Kant\'{e}, Mamadou Moustapha and Madelaine, Florent},
  title =	{{Weakly-Sparse and Strongly Flip-Flat Classes of Graphs Are Uniformly Almost-Wide}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.41},
  URN =		{urn:nbn:de:0030-drops-254668},
  doi =		{10.4230/LIPIcs.CSL.2026.41},
  annote =	{Keywords: Almost-wide, Flip-flatness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.13
Solving Partial Dominating Set and Related Problems Using Twin-Width

Authors: Jakub Balabán, Daniel Mock, and Peter Rossmanith

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are W[1]-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form ϕ≡∃ x₁⋯ ∃ x_k ∑_{α ∈ I} #y ψ_α(x₁,…,x_k,y) ≥ t, where ψ_α is a quantifier-free formula for each α ∈ I, t is an arbitrary number, and #y is a counting quantifier, can be evaluated in time f(d,k)n, where n is the number of vertices and d is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.
Cite as

Jakub Balabán, Daniel Mock, and Peter Rossmanith. Solving Partial Dominating Set and Related Problems Using Twin-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.13,
  author =	{Balab\'{a}n, Jakub and Mock, Daniel and Rossmanith, Peter},
  title =	{{Solving Partial Dominating Set and Related Problems Using Twin-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.13},
  URN =		{urn:nbn:de:0030-drops-241203},
  doi =		{10.4230/LIPIcs.MFCS.2025.13},
  annote =	{Keywords: Partial Dominating Set, Partial Vertex Cover, meta-algorithm, counting logic, twin-width}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.90
Elimination Distance to Dominated Clusters

Authors: Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
In the Dominated Cluster Deletion problem, we are given an undirected graph G and integers k and d and the question is to decide whether there exists a set of at most k vertices whose removal results in a graph in which each connected component has a dominating set of size at most d. In the Elimination Distance to Dominated Clusters problem, we are again given an undirected graph G and integers k and d and the question is to decide whether we can recursively delete vertices up to depth k such that each remaining connected component has a dominating set of size at most d. Bentert et al. [Bentert et al., MFCS 2024] recently provided an almost complete classification of the parameterized complexity of Dominated Cluster Deletion with respect to the parameters k, d, c, and Δ, where c and Δ are the degeneracy, and the maximum degree of the input graph, respectively. In particular, they provided a non-uniform algorithm with running time f(k,d)⋅ n^{𝒪(d)}. They left as an open problem whether the problem is fixed-parameter tractable with respect to the parameter k + d + c. We provide a uniform algorithm running in time f(k,d)⋅ n^{𝒪(d)} for both Dominated Cluster Deletion and Elimination Distance to Dominated Clusters. We furthermore show that both problems are FPT when parameterized by k+d+𝓁, where 𝓁 is the semi-ladder index of the input graph, a parameter that is upper bounded and may be much smaller than the degeneracy c, positively answering the open question of Bentert et al. We further complete the picture by providing an almost full classification for the parameterized complexity and kernelization complexity of Elimination Distance to Dominated Clusters. The one difficult base case that remains open is whether Treedepth (the case d = 0) is NP-hard on graphs of bounded maximum degree.
Cite as

Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny. Elimination Distance to Dominated Clusters. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 90:1-90:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schirrmacher_et_al:LIPIcs.MFCS.2025.90,
  author =	{Schirrmacher, Nicole and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Elimination Distance to Dominated Clusters}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{90:1--90:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.90},
  URN =		{urn:nbn:de:0030-drops-241978},
  doi =		{10.4230/LIPIcs.MFCS.2025.90},
  annote =	{Keywords: Graph theory, Fixed-parameter algorithms, Dominated cluster, Elimination distance}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.147
Separability Properties of Monadically Dependent Graph Classes

Authors: Édouard Bonnet, Samuel Braunfeld, Ioannis Eleftheriadis, Colin Geniet, Nikolas Mählmann, Michał Pilipczuk, Wojciech Przybyszewski, and Szymon Toruńczyk

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
A graph class 𝒞 is monadically dependent if one cannot interpret all graphs in colored graphs from 𝒞 using a fixed first-order interpretation. We prove that monadically dependent classes can be exactly characterized by the following property, which we call flip-separability: for every r ∈ ℕ, ε > 0, and every graph G ∈ 𝒞 equipped with a weight function on vertices, one can apply a bounded (in terms of 𝒞,r,ε) number of flips (complementations of the adjacency relation on a subset of vertices) to G so that in the resulting graph, every radius-r ball contains at most an ε-fraction of the total weight. On the way to this result, we introduce a robust toolbox for working with various notions of local separations in monadically dependent classes.
Cite as

Édouard Bonnet, Samuel Braunfeld, Ioannis Eleftheriadis, Colin Geniet, Nikolas Mählmann, Michał Pilipczuk, Wojciech Przybyszewski, and Szymon Toruńczyk. Separability Properties of Monadically Dependent Graph Classes. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 147:1-147:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.ICALP.2025.147,
  author =	{Bonnet, \'{E}douard and Braunfeld, Samuel and Eleftheriadis, Ioannis and Geniet, Colin and M\"{a}hlmann, Nikolas and Pilipczuk, Micha{\l} and Przybyszewski, Wojciech and Toru\'{n}czyk, Szymon},
  title =	{{Separability Properties of Monadically Dependent Graph Classes}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{147:1--147:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.147},
  URN =		{urn:nbn:de:0030-drops-235246},
  doi =		{10.4230/LIPIcs.ICALP.2025.147},
  annote =	{Keywords: Structural graph theory, Monadic dependence}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.167
Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO

Authors: Nikolas Mählmann

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The graph parameter shrub-depth is a dense analog of tree-depth. We characterize classes of bounded shrub-depth by forbidden induced subgraphs. The obstructions are well-controlled flips of large half-graphs and of disjoint unions of many long paths. Applying this characterization, we show that on every hereditary class of unbounded shrub-depth, MSO is more expressive than FO. This confirms a conjecture of [Gajarský and Hliněný; LMCS 2015] who proved that on classes of bounded shrub-depth FO and MSO have the same expressive power. Combined, the two results fully characterize the hereditary classes on which FO and MSO coincide, answering an open question by [Elberfeld, Grohe, and Tantau; LICS 2012]. Our work is inspired by the notion of stability from model theory. A graph class 𝒞 is MSO-stable, if no MSO-formula can define arbitrarily long linear orders in graphs from 𝒞. We show that a hereditary graph class is MSO-stable if and only if it has bounded shrub-depth. As a key ingredient, we prove that every hereditary class of unbounded shrub-depth FO-interprets the class of all paths. This improves upon a result of [Ossona de Mendez, Pilipczuk, and Siebertz; Eur. J. Comb. 2025] who showed the same statement for FO-transductions instead of FO-interpretations.
Cite as

Nikolas Mählmann. Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 167:1-167:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mahlmann:LIPIcs.ICALP.2025.167,
  author =	{M\"{a}hlmann, Nikolas},
  title =	{{Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{167:1--167:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.167},
  URN =		{urn:nbn:de:0030-drops-235444},
  doi =		{10.4230/LIPIcs.ICALP.2025.167},
  annote =	{Keywords: Shrub-Depth, Forbidden Induced Subgraphs, MSO, Stability Theory}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICDT.2025.3
Evaluating First-Order Formulas in Structured Graphs (Invited Talk)

Authors: Szymon Toruńczyk

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
A central problem in database theory concerns the complexity of the query evaluation problem, also called the model-checking problem in finite model theory: the problem of evaluating a given formula in a given structure. Here, I will focus on formulas of first-order logic, and the data complexity (or parameterized complexity) of their evaluation. Leveraging tools from structural graph theory, I will assume that the input structure is a graph which comes from a fixed class of well-structured graphs, such as the class of planar graphs, classes of bounded treewidth or clique-width, or much more general "tame" graph classes, such as the nowhere dense graph classes introduced by Ossona de Mendez and Nešetřil, or classes of bounded twin-width studied by Bonnet, Thomassé, and coauthors. I will survey the recent progress in this area, which connects tools from structural graph theory, from model theory - such as stability and dependence - and from statistical learning theory and computational geometry - such as VC-dimension and ε-nets.
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Szymon Toruńczyk. Evaluating First-Order Formulas in Structured Graphs (Invited Talk). In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{torunczyk:LIPIcs.ICDT.2025.3,
  author =	{Toru\'{n}czyk, Szymon},
  title =	{{Evaluating First-Order Formulas in Structured Graphs}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{3:1--3:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.3},
  URN =		{urn:nbn:de:0030-drops-229449},
  doi =		{10.4230/LIPIcs.ICDT.2025.3},
  annote =	{Keywords: Finite model theory, first-order model checking, graph parameters}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.21
Adjacency Labeling Schemes for Small Classes

Authors: Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A graph class admits an implicit representation if, for every positive integer n, its n-vertex graphs have a O(log n)-bit (adjacency) labeling scheme, i.e., their vertices can be labeled by binary strings of length O(log n) such that the presence of an edge between any pair of vertices can be deduced solely from their labels. The famous Implicit Graph Conjecture posited that every hereditary (i.e., closed under taking induced subgraphs) factorial (i.e., containing 2^O(n log n) n-vertex graphs) class admits an implicit representation. The conjecture was recently refuted [Hatami and Hatami, FOCS '22], and does not even hold among monotone (i.e., closed under taking subgraphs) factorial classes [Bonnet et al., ICALP '24]. However, monotone small (i.e., containing at most n! cⁿ many n-vertex graphs for some constant c) classes do admit implicit representations. This motivates the Small Implicit Graph Conjecture: Every hereditary small class admits an O(log n)-bit labeling scheme. We provide evidence supporting the Small Implicit Graph Conjecture. First, we show that every small weakly sparse (i.e., excluding some fixed bipartite complete graph as a subgraph) class has an implicit representation. This is a consequence of the following fact of independent interest proved in the paper: Every weakly sparse small class has bounded expansion (hence, in particular, bounded degeneracy). Second, we show that every hereditary small class admits an O(log³ n)-bit labeling scheme, which provides a substantial improvement of the best-known polynomial upper bound of n^(1-ε) on the size of adjacency labeling schemes for such classes. This is a consequence of another fact of independent interest proved in the paper: Every small class has neighborhood complexity O(n log n).
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev. Adjacency Labeling Schemes for Small Classes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.ITCS.2025.21,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor},
  title =	{{Adjacency Labeling Schemes for Small Classes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.21},
  URN =		{urn:nbn:de:0030-drops-226493},
  doi =		{10.4230/LIPIcs.ITCS.2025.21},
  annote =	{Keywords: Adjacency labeling, degeneracy, weakly sparse classes, small classes, implicit graph conjecture}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.6
Equi-Rank Homomorphism Preservation Theorem on Finite Structures

Authors: Benjamin Rossman

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
The Homomorphism Preservation Theorem (HPT) of classical model theory states that a first-order sentence is preserved under homomorphisms if, and only if, it is equivalent to an existential-positive sentence. This theorem remains valid when restricted to finite structures, as demonstrated by the author in [Rossman, 2008; Rossman, 2017] via distinct model-theoretic and circuit-complexity based proofs. In this paper, we present a third (and significantly simpler) proof of the finitary HPT based on a generalized Cai-Fürer-Immerman construction. This method establishes a tight correspondence between syntactic parameters of a homomorphism-preserved sentence (quantifier rank, variable width, alternation height) and structural parameters of its minimal models (tree-width, tree-depth, decomposition height). Consequently, we prove a conjectured "equi-rank" version of the finitary HPT. In contrast, previous versions of the finitary HPT possess additional properties, but incur blow-ups in the quantifier rank of the equivalent existential-positive sentence.
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Benjamin Rossman. Equi-Rank Homomorphism Preservation Theorem on Finite Structures. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rossman:LIPIcs.CSL.2025.6,
  author =	{Rossman, Benjamin},
  title =	{{Equi-Rank Homomorphism Preservation Theorem on Finite Structures}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.6},
  URN =		{urn:nbn:de:0030-drops-227634},
  doi =		{10.4230/LIPIcs.CSL.2025.6},
  annote =	{Keywords: finite model theory, preservation theorems, quantifier rank}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.7
Extension Preservation on Dense Graph Classes

Authors: Ioannis Eleftheriadis

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised to combinatorially tame classes of sparse structures [Atserias et al., JACM 2006; Atserias et al., SiCOMP 2008; Dawar, JCSS 2010; Dawar and Eleftheriadis, MFCS 2024]. In this article we initiate the study of preservation theorems for dense classes of graphs. In contrast to the sparse setting, we show that extension preservation fails on most natural dense classes of low complexity. Nonetheless, we isolate a technical condition which is sufficient for extension preservation to hold, providing a dense analogue to a result of [Atserias et al., SiCOMP 2008].
Cite as

Ioannis Eleftheriadis. Extension Preservation on Dense Graph Classes. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eleftheriadis:LIPIcs.CSL.2025.7,
  author =	{Eleftheriadis, Ioannis},
  title =	{{Extension Preservation on Dense Graph Classes}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.7},
  URN =		{urn:nbn:de:0030-drops-227640},
  doi =		{10.4230/LIPIcs.CSL.2025.7},
  annote =	{Keywords: Extension preservation, finite model theory, dense graphs, cliquewidth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.47
Preservation Theorems on Sparse Classes Revisited

Authors: Anuj Dawar and Ioannis Eleftheriadis

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We revisit the work studying homomorphism preservation for first-order logic in sparse classes of structures initiated in [Atserias et al., JACM 2006] and [Dawar, JCSS 2010]. These established that first-order logic has the homomorphism preservation property in any sparse class that is monotone and addable. It turns out that the assumption of addability is not strong enough for the proofs given. We demonstrate this by constructing classes of graphs of bounded treewidth which are monotone and addable but fail to have homomorphism preservation. We also show that homomorphism preservation fails on the class of planar graphs. On the other hand, the proofs of homomorphism preservation can be recovered by replacing addability by a stronger condition of amalgamation over bottlenecks. This is analogous to a similar condition formulated for extension preservation in [Atserias et al., SiCOMP 2008].
Cite as

Anuj Dawar and Ioannis Eleftheriadis. Preservation Theorems on Sparse Classes Revisited. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dawar_et_al:LIPIcs.MFCS.2024.47,
  author =	{Dawar, Anuj and Eleftheriadis, Ioannis},
  title =	{{Preservation Theorems on Sparse Classes Revisited}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{47:1--47:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.47},
  URN =		{urn:nbn:de:0030-drops-206036},
  doi =		{10.4230/LIPIcs.MFCS.2024.47},
  annote =	{Keywords: Homomorphism preservation, sparsity, finite model theory, planar graphs}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.119
Monadic NIP in Monotone Classes of Relational Structures

Authors: Samuel Braunfeld, Anuj Dawar, Ioannis Eleftheriadis, and Aris Papadopoulos

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We prove that for any monotone class of finite relational structures, the first-order theory of the class is NIP in the sense of stability theory if, and only if, the collection of Gaifman graphs of structures in this class is nowhere dense. This generalises results previously known for graphs to relational structures and answers an open question posed by Adler and Adler (2014). The result is established by the application of Ramsey-theoretic techniques and shows that the property of being NIP is highly robust for monotone classes. We also show that the model-checking problem for first-order logic is intractable on any monotone class of structures that is not (monadically) NIP. This is a contribution towards the conjecture that the hereditary classes of structures admitting fixed-parameter tractable model-checking are precisely those that are monadically NIP.
Cite as

Samuel Braunfeld, Anuj Dawar, Ioannis Eleftheriadis, and Aris Papadopoulos. Monadic NIP in Monotone Classes of Relational Structures. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 119:1-119:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{braunfeld_et_al:LIPIcs.ICALP.2023.119,
  author =	{Braunfeld, Samuel and Dawar, Anuj and Eleftheriadis, Ioannis and Papadopoulos, Aris},
  title =	{{Monadic NIP in Monotone Classes of Relational Structures}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{119:1--119:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.119},
  URN =		{urn:nbn:de:0030-drops-181712},
  doi =		{10.4230/LIPIcs.ICALP.2023.119},
  annote =	{Keywords: Model theory, finite model theory, structural graph theory, model-checking}
}
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