3 Search Results for "Biró, Péter"

Document
DOI: 10.4230/LIPIcs.MFCS.2023.8
Recognizing H-Graphs - Beyond Circular-Arc Graphs

Authors: Deniz Ağaoğlu Çağırıcı, Onur Çağırıcı, Jan Derbisz, Tim A. Hartmann, Petr Hliněný, Jan Kratochvíl, Tomasz Krawczyk, and Peter Zeman

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
In 1992 Biró, Hujter and Tuza introduced, for every fixed connected graph H, the class of H-graphs, defined as the intersection graphs of connected subgraphs of some subdivision of H. Such classes of graphs are related to many known graph classes: for example, K₂-graphs coincide with interval graphs, K₃-graphs with circular-arc graphs, the union of T-graphs, where T ranges over all trees, coincides with chordal graphs. Recently, quite a lot of research has been devoted to understanding the tractability border for various computational problems, such as recognition or isomorphism testing, in classes of H-graphs for different graphs H. In this work we undertake this research topic, focusing on the recognition problem. Chaplick, Töpfer, Voborník, and Zeman showed an XP-algorithm testing whether a given graph is a T-graph, where the parameter is the size of the tree T. In particular, for every fixed tree T the recognition of T-graphs can be solved in polynomial time. Tucker showed a polynomial time algorithm recognizing K₃-graphs (circular-arc graphs). On the other hand, Chaplick et al. showed also that for every fixed graph H containing two distinct cycles sharing an edge, the recognition of H-graphs is NP-hard. The main two results of this work narrow the gap between the NP-hard and 𝖯 cases of H-graph recognition. First, we show that the recognition of H-graphs is NP-hard when H contains two distinct cycles. On the other hand, we show a polynomial-time algorithm recognizing L-graphs, where L is a graph containing a cycle and an edge attached to it (which we call lollipop graphs). Our work leaves open the recognition problems of M-graphs for every unicyclic graph M different from a cycle and a lollipop.
Cite as

Deniz Ağaoğlu Çağırıcı, Onur Çağırıcı, Jan Derbisz, Tim A. Hartmann, Petr Hliněný, Jan Kratochvíl, Tomasz Krawczyk, and Peter Zeman. Recognizing H-Graphs - Beyond Circular-Arc Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{agaoglucagirici_et_al:LIPIcs.MFCS.2023.8,
  author =	{A\u{g}ao\u{g}lu \c{C}a\u{g}{\i}r{\i}c{\i}, Deniz and \c{C}a\u{g}{\i}r{\i}c{\i}, Onur and Derbisz, Jan and Hartmann, Tim A. and Hlin\v{e}n\'{y}, Petr and Kratochv{\'\i}l, Jan and Krawczyk, Tomasz and Zeman, Peter},
  title =	{{Recognizing H-Graphs - Beyond Circular-Arc Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.8},
  URN =		{urn:nbn:de:0030-drops-185420},
  doi =		{10.4230/LIPIcs.MFCS.2023.8},
  annote =	{Keywords: H-graphs, Intersection Graphs, Helly Property}
}
Document
DOI: 10.4230/DagRep.11.6.124
Matching Under Preferences: Theory and Practice (Dagstuhl Seminar 21301)

Authors: Haris Aziz, Péter Biró, Tamás Fleiner, and Bettina Klaus

Published in: Dagstuhl Reports, Volume 11, Issue 6 (2021)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 21301 "Matching Under Preferences: Theory and Practice". The seminar featured a mixture of technical scientific talks, survey talks, open problem presentations, working group sessions, five-minute contributions ("rump session"), and a panel discussion. This was the first Dagstuhl seminar that was dedicated to matching under preferences.
Cite as

Haris Aziz, Péter Biró, Tamás Fleiner, and Bettina Klaus. Matching Under Preferences: Theory and Practice (Dagstuhl Seminar 21301). In Dagstuhl Reports, Volume 11, Issue 6, pp. 124-146, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{aziz_et_al:DagRep.11.6.124,
  author =	{Aziz, Haris and Bir\'{o}, P\'{e}ter and Fleiner, Tam\'{a}s and Klaus, Bettina},
  title =	{{Matching Under Preferences: Theory and Practice (Dagstuhl Seminar 21301)}},
  pages =	{124--146},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{11},
  number =	{6},
  editor =	{Aziz, Haris and Bir\'{o}, P\'{e}ter and Fleiner, Tam\'{a}s and Klaus, Bettina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.6.124},
  URN =		{urn:nbn:de:0030-drops-155826},
  doi =		{10.4230/DagRep.11.6.124},
  annote =	{Keywords: market design, matching under preferences, matching with distributional constraints, organ exchange, stable matching}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.8
Recognizing Proper Tree-Graphs

Authors: Steven Chaplick, Petr A. Golovach, Tim A. Hartmann, and Dušan Knop

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

Abstract
We investigate the parameterized complexity of the recognition problem for the proper H-graphs. The H-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph H, and the properness means that the containment relationship between the representations of the vertices is forbidden. The class of H-graphs was introduced as a natural (parameterized) generalization of interval and circular-arc graphs by Biró, Hujter, and Tuza in 1992, and the proper H-graphs were introduced by Chaplick et al. in WADS 2019 as a generalization of proper interval and circular-arc graphs. For these graph classes, H may be seen as a structural parameter reflecting the distance of a graph to a (proper) interval graph, and as such gained attention as a structural parameter in the design of efficient algorithms. We show the following results. - For a tree T with t nodes, it can be decided in 2^{𝒪(t² log t)} ⋅ n³ time, whether an n-vertex graph G is a proper T-graph. For yes-instances, our algorithm outputs a proper T-representation. This proves that the recognition problem for proper H-graphs, where H required to be a tree, is fixed-parameter tractable when parameterized by the size of T. Previously only NP-completeness was known. - Contrasting to the first result, we prove that if H is not constrained to be a tree, then the recognition problem becomes much harder. Namely, we show that there is a multigraph H with 4 vertices and 5 edges such that it is NP-complete to decide whether G is a proper H-graph.
Cite as

Steven Chaplick, Petr A. Golovach, Tim A. Hartmann, and Dušan Knop. Recognizing Proper Tree-Graphs. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chaplick_et_al:LIPIcs.IPEC.2020.8,
  author =	{Chaplick, Steven and Golovach, Petr A. and Hartmann, Tim A. and Knop, Du\v{s}an},
  title =	{{Recognizing Proper Tree-Graphs}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{8:1--8:15},
  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.2020.8},
  URN =		{urn:nbn:de:0030-drops-133118},
  doi =		{10.4230/LIPIcs.IPEC.2020.8},
  annote =	{Keywords: intersection graphs, H-graphs, recognition, fixed-parameter tractability}
}
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