Detailed Information on Publication Record
2023
Recognizing H-Graphs - Beyond Circular-Arc Graphs
AGAOGLU CAGIRICI, Deniz, Onur CAGIRICI, Jan DERBISZ, Tim HARTMANN, Petr HLINĚNÝ et. al.Basic information
Original name
Recognizing H-Graphs - Beyond Circular-Arc Graphs
Authors
AGAOGLU CAGIRICI, Deniz (792 Turkey, belonging to the institution), Onur CAGIRICI (792 Turkey), Jan DERBISZ (616 Poland), Tim HARTMANN (276 Germany), Petr HLINĚNÝ (203 Czech Republic, guarantor, belonging to the institution), Jan KRATOCHVÍL (203 Czech Republic), Tomasz KRAWCZYK (616 Poland) and Peter ZEMAN (703 Slovakia)
Edition
Dagstuhl, Germany, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023), p. "8:1"-"8:14", 14 pp. 2023
Publisher
Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik
Other information
Language
English
Type of outcome
Stať ve sborníku
Field of Study
10201 Computer sciences, information science, bioinformatics
Country of publisher
Germany
Confidentiality degree
není předmětem státního či obchodního tajemství
Publication form
electronic version available online
RIV identification code
RIV/00216224:14330/23:00131122
Organization unit
Faculty of Informatics
ISBN
978-3-95977-292-1
ISSN
Keywords in English
H-graphs; Intersection Graphs; Helly Property
Tags
Změněno: 7/4/2024 23:06, RNDr. Pavel Šmerk, Ph.D.
Abstract
V originále
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.
Links
| MUNI/A/1081/2022, interní kód MU |
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| MUNI/A/1433/2022, interní kód MU |
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