List Covering of Regular Multigraphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455444" target="_blank" >RIV/00216208:11320/22:10455444 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-06678-8_17" target="_blank" >https://doi.org/10.1007/978-3-031-06678-8_17</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-06678-8_17" target="_blank" >10.1007/978-3-031-06678-8_17</a>

Jazyk výsledku

angličtina

Název v původním jazyce

List Covering of Regular Multigraphs

Popis výsledku v původním jazyce

A graph covering projection, also known as a locally bijective homomorphism, is a mapping between vertices and edges of two graphs which preserves incidencies and is a local bijection. This notion stems from topological graph theory, but has also found applications in combinatorics and theoretical computer science. It has been known that for every fixed simple regular graph H of valency greater than 2, deciding if an input graph covers H is NPcomplete. In recent years, topological graph theory has developed into heavily relying on multiple edges, loops, and semi-edges, but only partial results on the complexity of covering multigraphs with semi-edges are known so far. In this paper we consider the list version of the problem, called List-H-Cover, where the vertices and edges of the input graph come with lists of admissible targets. Our main result reads that the List-H-Cover problem is NP-complete for every regular multigraph H of valency greater than 2 which contains at least one semi-simple vertex (i.e., a vertex which is incident with no loops, with no multiple edges and with at most one semi-edge). Using this result we almost show the NP-co/polytime dichotomy for the computational complexity of ListH-Cover of cubic multigraphs, leaving just five open cases.

Název v anglickém jazyce

List Covering of Regular Multigraphs

Popis výsledku anglicky

A graph covering projection, also known as a locally bijective homomorphism, is a mapping between vertices and edges of two graphs which preserves incidencies and is a local bijection. This notion stems from topological graph theory, but has also found applications in combinatorics and theoretical computer science. It has been known that for every fixed simple regular graph H of valency greater than 2, deciding if an input graph covers H is NPcomplete. In recent years, topological graph theory has developed into heavily relying on multiple edges, loops, and semi-edges, but only partial results on the complexity of covering multigraphs with semi-edges are known so far. In this paper we consider the list version of the problem, called List-H-Cover, where the vertices and edges of the input graph come with lists of admissible targets. Our main result reads that the List-H-Cover problem is NP-complete for every regular multigraph H of valency greater than 2 which contains at least one semi-simple vertex (i.e., a vertex which is incident with no loops, with no multiple edges and with at most one semi-edge). Using this result we almost show the NP-co/polytime dichotomy for the computational complexity of ListH-Cover of cubic multigraphs, leaving just five open cases.

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/GA20-15576S" target="_blank" >GA20-15576S: Nakrývání grafů: Symetrie a složitost</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

COMBINATORIAL ALGORITHMS (IWOCA 2022)

ISBN

978-3-031-06677-1

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

15

Strana od-do

228-242

Název nakladatele

SPRINGER INTERNATIONAL PUBLISHING AG

Místo vydání

CHAM

Místo konání akce

Univ Trier

Datum konání akce

7. 6. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000876353400017