Recognition and Isomorphism of Proper H-Graphs for Unicyclic H in FPT-Time

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00139777" target="_blank" >RIV/00216224:14330/24:00139777 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-981-97-0566-5_22" target="_blank" >http://dx.doi.org/10.1007/978-981-97-0566-5_22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-981-97-0566-5_22" target="_blank" >10.1007/978-981-97-0566-5_22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Recognition and Isomorphism of Proper H-Graphs for Unicyclic H in FPT-Time

Popis výsledku v původním jazyce

An H-graph is an intersection graph of connected subgraphs of a suitable subdivision of a fixed graph H. Many important classes of graphs can be expressed as H-graphs, and in particular, every graph is an H-graph for a suitable graph H. An H-graph is called proper if it has a representation where no subgraph properly contains another. We consider the recognition and isomorphism problems for proper U-graphs where U is a unicyclic graph, i.e. a graph which contains exactly one cycle. We prove that testing whether a graph is a (proper) U-graph, for some U, is NP-hard. On the positive side, we give an FPT-time recognition algorithm for a fixed U, parameterized by |U|. As an application, we obtain an FPT-time isomorphism algorithm for proper U-graphs, parameterized by |U|. To complement this, we prove that the isomorphism problem for (proper) H-graphs is GI-complete for every fixed H which is not unicyclic nor a tree.

Název v anglickém jazyce

Recognition and Isomorphism of Proper H-Graphs for Unicyclic H in FPT-Time

Popis výsledku anglicky

An H-graph is an intersection graph of connected subgraphs of a suitable subdivision of a fixed graph H. Many important classes of graphs can be expressed as H-graphs, and in particular, every graph is an H-graph for a suitable graph H. An H-graph is called proper if it has a representation where no subgraph properly contains another. We consider the recognition and isomorphism problems for proper U-graphs where U is a unicyclic graph, i.e. a graph which contains exactly one cycle. We prove that testing whether a graph is a (proper) U-graph, for some U, is NP-hard. On the positive side, we give an FPT-time recognition algorithm for a fixed U, parameterized by |U|. As an application, we obtain an FPT-time isomorphism algorithm for proper U-graphs, parameterized by |U|. To complement this, we prove that the isomorphism problem for (proper) H-graphs is GI-complete for every fixed H which is not unicyclic nor a tree.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA20-04567S" target="_blank" >GA20-04567S: Struktura efektivně řešitelných případů těžkých algoritmických problémů na grafech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024

ISBN

9789819705658

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

15

Strana od-do

304-318

Název nakladatele

Springer

Místo vydání

Kanazawa, Japan

Místo konání akce

Kanazawa, Japan

Datum konání akce

1. 1. 2024

Typ akce podle státní příslušnosti

CST - Celostátní akce

Kód UT WoS článku

001207267500022