List Locally Surjective Homomorphisms in Hereditary Graph Classes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453198" target="_blank" >RIV/00216208:11320/22:10453198 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.ISAAC.2022.30" target="_blank" >https://doi.org/10.4230/LIPIcs.ISAAC.2022.30</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2022.30" target="_blank" >10.4230/LIPIcs.ISAAC.2022.30</a>

Jazyk výsledku

angličtina

Název v původním jazyce

List Locally Surjective Homomorphisms in Hereditary Graph Classes

Popis výsledku v původním jazyce

A locally surjective homomorphism from a graph G to a graph H is an edge-preserving mapping from V (G) to V (H) that is surjective in the neighborhood of each vertex in G. In the list locally surjective homomorphism problem, denoted by LLSHom(H), the graph H is fixed and the instance consists of a graph G whose every vertex is equipped with a subset of V (H), called list. We ask for the existence of a locally surjective homomorphism from G to H, where every vertex of G is mapped to a vertex from its list. In this paper, we study the complexity of the LLSHom(H) problem in F-free graphs, i.e., graphs that exclude a fixed graph F as an induced subgraph. We aim to understand for which pairs (H, F) the problem can be solved in subexponential time. We show that for all graphs H, for which the problem is NP-hard in general graphs, it cannot be solved in subexponential time in F-free graphs for F being a bounded-degree forest, unless the ETH fails. The initial study reveals that a natural subfamily of bounded-degree forests F, that might lead to some tractability results, is the family S consisting of forests whose every component has at most three leaves. In this case, we exhibit the following dichotomy theorem: besides the cases that are polynomial-time solvable in general graphs, the graphs H in {P3, C4} are the only connected ones that allow for a subexponential-time algorithm in F-free graphs for every F in S (unless the ETH fails).

Název v anglickém jazyce

List Locally Surjective Homomorphisms in Hereditary Graph Classes

Popis výsledku anglicky

A locally surjective homomorphism from a graph G to a graph H is an edge-preserving mapping from V (G) to V (H) that is surjective in the neighborhood of each vertex in G. In the list locally surjective homomorphism problem, denoted by LLSHom(H), the graph H is fixed and the instance consists of a graph G whose every vertex is equipped with a subset of V (H), called list. We ask for the existence of a locally surjective homomorphism from G to H, where every vertex of G is mapped to a vertex from its list. In this paper, we study the complexity of the LLSHom(H) problem in F-free graphs, i.e., graphs that exclude a fixed graph F as an induced subgraph. We aim to understand for which pairs (H, F) the problem can be solved in subexponential time. We show that for all graphs H, for which the problem is NP-hard in general graphs, it cannot be solved in subexponential time in F-free graphs for F being a bounded-degree forest, unless the ETH fails. The initial study reveals that a natural subfamily of bounded-degree forests F, that might lead to some tractability results, is the family S consisting of forests whose every component has at most three leaves. In this case, we exhibit the following dichotomy theorem: besides the cases that are polynomial-time solvable in general graphs, the graphs H in {P3, C4} are the only connected ones that allow for a subexponential-time algorithm in F-free graphs for every F in S (unless the ETH fails).

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/GN22-14872O" target="_blank" >GN22-14872O: Kombinatorické metody v teorii informace</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

33rd International Symposium on Algorithms and Computation (ISAAC 2022)

ISBN

978-3-95977-258-7

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

15

Strana od-do

1-15

Název nakladatele

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik

Místo vydání

Dagstuhl

Místo konání akce

Seoul, Korea

Datum konání akce

19. 12. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—