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Complete Volume

**Published in:** LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

LIPIcs, Volume 138, MFCS'19, Complete Volume

44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Proceedings{rossmanith_et_al:LIPIcs.MFCS.2019, title = {{LIPIcs, Volume 138, MFCS'19, Complete Volume}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019}, URN = {urn:nbn:de:0030-drops-112092}, doi = {10.4230/LIPIcs.MFCS.2019}, annote = {Keywords: Theory of computation} }

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Front Matter

**Published in:** LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Front Matter, Table of Contents, Preface, Conference Organization

44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rossmanith_et_al:LIPIcs.MFCS.2019.0, author = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {0:i--0:xvi}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.0}, URN = {urn:nbn:de:0030-drops-109444}, doi = {10.4230/LIPIcs.MFCS.2019.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

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**Published in:** LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its internal vertices have distinct colors. We say that the graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. We study the problem of deciding whether the vertices of a given graph can be colored with at most k colors so that the graph becomes rainbow vertex-connected. Although edge-colorings have been studied extensively under similar constraints, there are significantly fewer results on the vertex variant that we consider. In particular, its complexity on structured graph classes was explicitly posed as an open question.
We show that the problem remains NP-complete even on bipartite apex graphs and on split graphs. The former can be seen as a first step in the direction of studying the complexity of rainbow coloring on sparse graphs, an open problem which has attracted attention but limited progress. We also give hardness of approximation results for both bipartite and split graphs. To complement the negative results, we show that bipartite permutation graphs, interval graphs, and block graphs can be rainbow vertex-connected optimally in polynomial time.

Pinar Heggernes, Davis Issac, Juho Lauri, Paloma T. Lima, and Erik Jan van Leeuwen. Rainbow Vertex Coloring Bipartite Graphs and Chordal Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 83:1-83:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{heggernes_et_al:LIPIcs.MFCS.2018.83, author = {Heggernes, Pinar and Issac, Davis and Lauri, Juho and Lima, Paloma T. and van Leeuwen, Erik Jan}, title = {{Rainbow Vertex Coloring Bipartite Graphs and Chordal Graphs}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {83:1--83:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.83}, URN = {urn:nbn:de:0030-drops-96657}, doi = {10.4230/LIPIcs.MFCS.2018.83}, annote = {Keywords: Rainbow coloring, graph classes, polynomial-time algorithms, approximation algorithms} }

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**Published in:** LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)

Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study of the Strong F-closure problem, where F is a fixed graph. This is a generalization of Strong Triadic Closure, whereas it is a relaxation of F-free Edge Deletion. In Strong F-closure, we want to select a maximum number of edges of the input graph G, and mark them as strong edges, in the following way: whenever a subset of the strong edges forms a subgraph isomorphic to F, then the corresponding induced subgraph of G is not isomorphic to F. Hence the subgraph of G defined by the strong edges is not necessarily F-free, but whenever it contains a copy of F, there are additional edges in G to destroy that strong copy of F in G.
We study Strong F-closure from a parameterized perspective with various natural parameterizations. Our main focus is on the number k of strong edges as the parameter. We show that the problem is FPT with this parameterization for every fixed graph F, whereas it does not admit a polynomial kernel even when F =P_3. In fact, this latter case is equivalent to the Strong Triadic Closure problem, which motivates us to study this problem on input graphs belonging to well known graph classes. We show that Strong Triadic Closure does not admit a polynomial kernel even when the input graph is a split graph, whereas it admits a polynomial kernel when the input graph is planar, and even d-degenerate. Furthermore, on graphs of maximum degree at most 4, we show that Strong Triadic Closure is FPT with the above guarantee parameterization k - mu(G), where mu(G) is the maximum matching size of G. We conclude with some results on the parameterization of Strong F-closure by the number of edges of G that are not selected as strong.

Petr A. Golovach, Pinar Heggernes, Athanasios L. Konstantinidis, Paloma T. Lima, and Charis Papadopoulos. Parameterized Aspects of Strong Subgraph Closure. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{golovach_et_al:LIPIcs.SWAT.2018.23, author = {Golovach, Petr A. and Heggernes, Pinar and Konstantinidis, Athanasios L. and Lima, Paloma T. and Papadopoulos, Charis}, title = {{Parameterized Aspects of Strong Subgraph Closure}}, booktitle = {16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)}, pages = {23:1--23:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-068-2}, ISSN = {1868-8969}, year = {2018}, volume = {101}, editor = {Eppstein, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.23}, URN = {urn:nbn:de:0030-drops-88490}, doi = {10.4230/LIPIcs.SWAT.2018.23}, annote = {Keywords: Strong triadic closure, Parameterized complexity, Forbidden subgraphs} }

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**Published in:** LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within the traditional P vs NP dichotomy and within parameterized complexity. The Pi-Subgraph problem asks whether an input graph contains an induced subgraph on at least k vertices satisfying graph property Pi. For many applications, it is desirable that the found subgraph has as few connections to the rest of the graph as possible, which gives rise to the Secluded Pi-Subgraph problem. Here, input k is the size of the desired subgraph, and input t is a limit on the number of neighbors this subgraph has in the rest of the graph. This problem has been studied from a parameterized perspective, and unfortunately it turns out to be W[1]-hard for many graph properties Pi, even when parameterized by k+t. We show that the situation changes when we are looking for a connected induced subgraph satisfying Pi. In particular, we show that the Connected Secluded Pi-Subgraph problem is FPT when parameterized by just t for many important graph properties Pi.

Petr A. Golovach, Pinar Heggernes, Paloma T. Lima, and Pedro Montealegre. Finding Connected Secluded Subgraphs. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{golovach_et_al:LIPIcs.IPEC.2017.18, author = {Golovach, Petr A. and Heggernes, Pinar and Lima, Paloma T. and Montealegre, Pedro}, title = {{Finding Connected Secluded Subgraphs}}, booktitle = {12th International Symposium on Parameterized and Exact Computation (IPEC 2017)}, pages = {18:1--18:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-051-4}, ISSN = {1868-8969}, year = {2018}, volume = {89}, editor = {Lokshtanov, Daniel and Nishimura, Naomi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.18}, URN = {urn:nbn:de:0030-drops-85623}, doi = {10.4230/LIPIcs.IPEC.2017.18}, annote = {Keywords: Secluded subgraph, forbidden subgraphs, parameterized complexity} }

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**Published in:** LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)

Listing, generating or enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality. We establish enumeration algorithms as well as lower and upper bounds for the maximum number of minimal connected dominating sets in such graphs. In particular, we present algorithms to enumerate all minimal connected dominating sets of chordal graphs in time O(1.7159^n), of split graphs in time O(1.3803^n), and of AT-free, strongly chordal, and distance-hereditary graphs in time O^*(3^{n/3}), where n is the number of vertices of the input graph. Our algorithms imply corresponding upper bounds for the number of minimal connected dominating sets for these graph classes.

Petr A. Golovach, Pinar Heggernes, and Dieter Kratsch. Enumerating Minimal Connected Dominating Sets in Graphs of Bounded Chordality. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 307-318, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{golovach_et_al:LIPIcs.IPEC.2015.307, author = {Golovach, Petr A. and Heggernes, Pinar and Kratsch, Dieter}, title = {{Enumerating Minimal Connected Dominating Sets in Graphs of Bounded Chordality}}, booktitle = {10th International Symposium on Parameterized and Exact Computation (IPEC 2015)}, pages = {307--318}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-92-7}, ISSN = {1868-8969}, year = {2015}, volume = {43}, editor = {Husfeldt, Thore and Kanj, Iyad}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.307}, URN = {urn:nbn:de:0030-drops-55925}, doi = {10.4230/LIPIcs.IPEC.2015.307}, annote = {Keywords: Minimal connected dominating set, exact algorithms, enumeration} }

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**Published in:** Dagstuhl Reports, Volume 4, Issue 2 (2014)

This report documents the program and the outcomes of Dagstuhl Seminar 14071 "Graph Modification Problems". The seminar was held from February 9 to February 14, 2014. This report contains abstracts for presentations about the recent
developments on algorithms and structural results for graph modification problems, as well as related areas. Furthermore, the report contains a summary of open problems in this area of research.

Hans L. Bodlaender, Pinar Heggernes, and Daniel Lokshtanov. Graph Modification Problems (Dagstuhl Seminar 14071). In Dagstuhl Reports, Volume 4, Issue 2, pp. 38-59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Article{bodlaender_et_al:DagRep.4.2.38, author = {Bodlaender, Hans L. and Heggernes, Pinar and Lokshtanov, Daniel}, title = {{Graph Modification Problems (Dagstuhl Seminar 14071)}}, pages = {38--59}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2014}, volume = {4}, number = {2}, editor = {Bodlaender, Hans L. and Heggernes, Pinar and Lokshtanov, Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.4.2.38}, URN = {urn:nbn:de:0030-drops-45443}, doi = {10.4230/DagRep.4.2.38}, annote = {Keywords: graphs, algorithms, graph modification, fixed parameter tractable, graph classes} }

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**Published in:** LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

We initiate the study of the Bipartite Contraction problem from the perspective of parameterized complexity. In this problem we are given a graph G on n vertices and an integer k, and the task is to determine whether we can obtain a bipartite graph from G by a sequence of at most k edge contractions. Our main result is an f(k) n^{O(1)} time algorithm for Bipartite Contraction. Despite a strong resemblance between Bipartite Contraction and the classical Odd Cycle Transversal (OCT) problem, the methods developed to tackle OCT do not seem to be directly applicable to Bipartite Contraction. To obtain our result, we combine several techniques and concepts that are central in parameterized complexity: iterative compression, irrelevant vertex, and important separators. To the best of our knowledge, this is the first time the irrelevant vertex technique and the concept of important separators are applied in unison. Furthermore, our algorithm may serve as a comprehensible example of the usage of the irrelevant vertex technique.

Pinar Heggernes, Pim van 't Hof, Daniel Lokshtanov, and Christophe Paul. Obtaining a Bipartite Graph by Contracting Few Edges. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 217-228, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{heggernes_et_al:LIPIcs.FSTTCS.2011.217, author = {Heggernes, Pinar and van 't Hof, Pim and Lokshtanov, Daniel and Paul, Christophe}, title = {{Obtaining a Bipartite Graph by Contracting Few Edges}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {217--228}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-34-7}, ISSN = {1868-8969}, year = {2011}, volume = {13}, editor = {Chakraborty, Supratik and Kumar, Amit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.217}, URN = {urn:nbn:de:0030-drops-33579}, doi = {10.4230/LIPIcs.FSTTCS.2011.217}, annote = {Keywords: fixed parameter tractability, graph modification problems, edge contractions, bipartite graphs} }

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**Published in:** Dagstuhl Reports, Volume 1, Issue 5 (2011)

This report documents the program and the outcomes of Dagstuhl Seminar 11182 ``Exploiting graph structure to cope with hard problems'' which has been held in Schloss Dagstuhl -- Leibniz Center for Informatics from May 1st, 2011 to May 6th, 2011.
During the seminar experts with a common focus on graph algorithms presented various new results in how to attack NP-hard graph problems by using the structure of the input graph.
Moreover, in the afternoon of each seminar's day new problems have been posed and discussed.

Andreas Brandstädt, Martin Charles Golumbic, Pinar Heggernes, and Ross McConnell. Exploiting graph structure to cope with hard problems (Dagstuhl Seminar 11182). In Dagstuhl Reports, Volume 1, Issue 5, pp. 29-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@Article{brandstadt_et_al:DagRep.1.5.29, author = {Brandst\"{a}dt, Andreas and Golumbic, Martin Charles and Heggernes, Pinar and McConnell, Ross}, title = {{Exploiting graph structure to cope with hard problems (Dagstuhl Seminar 11182)}}, pages = {29--46}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2011}, volume = {1}, number = {5}, editor = {Brandst\"{a}dt, Andreas and Golumbic, Martin Charles and Heggernes, Pinar and McConnell, Ross}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.1.5.29}, URN = {urn:nbn:de:0030-drops-32027}, doi = {10.4230/DagRep.1.5.29}, annote = {Keywords: Graph Classes, Graph Algorithms, NP-completeness, Width Parameters, Approximation Algorithms, Parameterized Complexity} }

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