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Documents authored by Munaro, Andrea

Document
DOI: 10.4230/LIPIcs.ESA.2025.40
Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs

Authors: Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We show that, for every fixed positive integers r and k, Max-Weight List r-Colorable Induced Subgraph admits a polynomial-time algorithm on kP₃-free graphs. This problem is a common generalization of Max-Weight Independent Set, Odd Cycle Transversal and List r-Coloring, among others. Our result has several consequences. First, it implies that, for every fixed r ≥ 5, assuming 𝖯 ≠ NP, Max-Weight List r-Colorable Induced Subgraph is polynomial-time solvable on H-free graphs if and only if H is an induced subgraph of either kP₃ or P₅+kP₁, for some k ≥ 1. Second, it makes considerable progress toward a complexity dichotomy for Odd Cycle Transversal on H-free graphs, allowing to answer a question of Agrawal, Lima, Lokshtanov, Rzążewski, Saurabh, and Sharma [ACM Trans. Algorithms 2025]. Third, it gives a short and self-contained proof of the known result of Chudnovsky, Hajebi, and Spirkl [Combinatorica 2024] that List r-Coloring on kP₃-free graphs is polynomial-time solvable for every fixed r and k. We also consider two natural distance-d generalizations of Max-Weight Independent Set and List r-Coloring and provide polynomial-time algorithms on kP₃-free graphs for every fixed integers r, k, and d ≥ 6.
Cite as

Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi. Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galby_et_al:LIPIcs.ESA.2025.40,
  author =	{Galby, Esther and Lima, Paloma T. and Munaro, Andrea and Nikabadi, Amir},
  title =	{{Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{40:1--40:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.40},
  URN =		{urn:nbn:de:0030-drops-245086},
  doi =		{10.4230/LIPIcs.ESA.2025.40},
  annote =	{Keywords: Hereditary classes, list coloring, odd cycle transversal, independent set}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.34
Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs

Authors: Esther Galby, Andrea Munaro, and Shizhou Yang

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
We investigate a relaxation of the notion of treewidth-fragility, namely tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for independent packing problems on fractionally tree-independence-number-fragile graph classes. Our approach unifies and extends several known polynomial-time approximation schemes on seemingly unrelated graph classes, such as classes of intersection graphs of fat objects in a fixed dimension or proper minor-closed classes. We also study the related notion of layered tree-independence number, a relaxation of layered treewidth.
Cite as

Esther Galby, Andrea Munaro, and Shizhou Yang. Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{galby_et_al:LIPIcs.SoCG.2023.34,
  author =	{Galby, Esther and Munaro, Andrea and Yang, Shizhou},
  title =	{{Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.34},
  URN =		{urn:nbn:de:0030-drops-178840},
  doi =		{10.4230/LIPIcs.SoCG.2023.34},
  annote =	{Keywords: Independent packings, intersection graphs, polynomial-time approximation schemes, tree-independence number}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.6
Bounding the Mim-Width of Hereditary Graph Classes

Authors: Nick Brettell, Jake Horsfield, Andrea Munaro, Giacomo Paesani, and Daniël Paulusma

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
A large number of NP-hard graph problems are solvable in XP time when parameterized by some width parameter. Hence, when solving problems on special graph classes, it is helpful to know if the graph class under consideration has bounded width. In this paper we consider mim-width, a particularly general width parameter that has a number of algorithmic applications whenever a decomposition is "quickly computable" for the graph class under consideration. We start by extending the toolkit for proving (un)boundedness of mim-width of graph classes. By combining our new techniques with known ones we then initiate a systematic study into bounding mim-width from the perspective of hereditary graph classes, and make a comparison with clique-width, a more restrictive width parameter that has been well studied. We prove that for a given graph H, the class of H-free graphs has bounded mim-width if and only if it has bounded clique-width. We show that the same is not true for (H₁,H₂)-free graphs. We identify several general classes of (H₁,H₂)-free graphs having unbounded clique-width, but bounded mim-width, illustrating the power of mim-width. Moreover, we show that a branch decomposition of constant mim-width can be found in polynomial time, for these classes. Hence, as mentioned, these results have algorithmic implications: when the input is restricted to such a class of (H₁,H₂)-free graphs, many problems become polynomial-time solvable, including classical problems such as k-Colouring and Independent Set, domination-type problems known as LC-VSVP problems, and distance versions of LC-VSVP problems, to name just a few. We also prove a number of new results showing that, for certain H₁ and H₂, the class of (H₁,H₂)-free graphs has unbounded mim-width. Boundedness of clique-width implies boundedness of mim-width. By combining our results, which give both new bounded and unbounded cases for mim-width, with the known bounded cases for clique-width, we present summary theorems of the current state of the art for the boundedness of mim-width for (H₁,H₂)-free graphs. In particular, we classify the mim-width of (H₁,H₂)-free graphs for all pairs (H₁,H₂) with |V(H₁)| + |V(H₂)| ≤ 8. When H₁ and H₂ are connected graphs, we classify all pairs (H₁,H₂) except for one remaining infinite family and a few isolated cases.
Cite as

Nick Brettell, Jake Horsfield, Andrea Munaro, Giacomo Paesani, and Daniël Paulusma. Bounding the Mim-Width of Hereditary Graph Classes. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brettell_et_al:LIPIcs.IPEC.2020.6,
  author =	{Brettell, Nick and Horsfield, Jake and Munaro, Andrea and Paesani, Giacomo and Paulusma, Dani\"{e}l},
  title =	{{Bounding the Mim-Width of Hereditary Graph Classes}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.6},
  URN =		{urn:nbn:de:0030-drops-133099},
  doi =		{10.4230/LIPIcs.IPEC.2020.6},
  annote =	{Keywords: Width parameter, mim-width, clique-width, hereditary graph class}
}
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