Recognizing H-Graphs - Beyond Circular-Arc Graphs

D 2023

Recognizing H-Graphs - Beyond Circular-Arc Graphs

AGAOGLU CAGIRICI, Deniz, Onur CAGIRICI, Jan DERBISZ, Tim HARTMANN, Petr HLINĚNÝ et. al.

Základní údaje

Originální název

Recognizing H-Graphs - Beyond Circular-Arc Graphs

Autoři

AGAOGLU CAGIRICI, Deniz (792 Turecko, domácí), Onur CAGIRICI (792 Turecko), Jan DERBISZ (616 Polsko), Tim HARTMANN (276 Německo), Petr HLINĚNÝ (203 Česká republika, garant, domácí), Jan KRATOCHVÍL (203 Česká republika), Tomasz KRAWCZYK (616 Polsko) a Peter ZEMAN (703 Slovensko)

Vydání

Dagstuhl, Germany, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023), od s. "8:1"-"8:14", 14 s. 2023

Nakladatel

Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Kód RIV

RIV/00216224:14330/23:00131122

Organizační jednotka

Fakulta informatiky

ISBN

978-3-95977-292-1

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.MFCS.2023.8

Klíčová slova anglicky

H-graphs; Intersection Graphs; Helly Property

Štítky

core_A, firank_A, formela-conference

Změněno: 7. 4. 2024 23:06, RNDr. Pavel Šmerk, Ph.D.

Anotace

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.

Návaznosti

MUNI/A/1081/2022, interní kód MU

Název: Modelování, analýza a verifikace (2023)

Investor: Masarykova univerzita, Modelování, analýza a verifikace (2023)

MUNI/A/1433/2022, interní kód MU

Název: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 23

Investor: Masarykova univerzita, Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 23

Citovat

AGAOGLU CAGIRICI, Deniz, Onur CAGIRICI, Jan DERBISZ, Tim HARTMANN, Petr HLINĚNÝ, Jan KRATOCHVÍL, Tomasz KRAWCZYK a Peter ZEMAN. Recognizing H-Graphs - Beyond Circular-Arc Graphs. Online. In Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David. 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik, 2023, s. "8:1"-"8:14", 14 s. ISBN 978-3-95977-292-1. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.MFCS.2023.8.

@inproceedings{2294854,
   author = {Agaoglu Cagirici, Deniz and Cagirici, Onur and Derbisz, Jan and Hartmann, Tim and Hliněný, Petr and Kratochvíl, Jan and Krawczyk, Tomasz and Zeman, Peter},
   address = {Dagstuhl, Germany},
   booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
   doi = {http://dx.doi.org/10.4230/LIPIcs.MFCS.2023.8},
   editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
   keywords = {H-graphs; Intersection Graphs; Helly Property},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Dagstuhl, Germany},
   isbn = {978-3-95977-292-1},
   pages = {"8:1"-"8:14"},
   publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
   title = {Recognizing H-Graphs - Beyond Circular-Arc Graphs},
   year = {2023}
}

TY  - JOUR
ID  - 2294854
AU  - Agaoglu Cagirici, Deniz - Cagirici, Onur - Derbisz, Jan - Hartmann, Tim - Hliněný, Petr - Kratochvíl, Jan - Krawczyk, Tomasz - Zeman, Peter
PY  - 2023
TI  - Recognizing H-Graphs - Beyond Circular-Arc Graphs
PB  - Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik
CY  - Dagstuhl, Germany
SN  - 9783959772921
KW  - H-graphs
KW  - Intersection Graphs
KW  - Helly Property
N2  - 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.
ER  -

AGAOGLU CAGIRICI, Deniz, Onur CAGIRICI, Jan DERBISZ, Tim HARTMANN, Petr HLINĚNÝ, Jan KRATOCHVÍL, Tomasz KRAWCZYK a Peter ZEMAN. Recognizing H-Graphs - Beyond Circular-Arc Graphs. Online. In Leroux, J$\backslash$'$\{$e$\}$r$\backslash$\^{}$\{$o$\}$me and Lombardy, Sylvain and Peleg, David. \textit{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}. Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum f$\{\backslash$''u$\}$r Informatik, 2023, s.~''8:1''-''8:14'', 14 s. ISBN~978-3-95977-292-1. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.MFCS.2023.8.

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