List Locally Surjective Homomorphisms in Hereditary Graph Classes

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

List Locally Surjective Homomorphisms in Hereditary Graph Classes

Original language description

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).

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

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

Project

<a href="/en/project/GN22-14872O" target="_blank" >GN22-14872O: Combinatorial Methods in Information Theory</a><br>

Continuities

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

Publication year

2022

Confidentiality

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

Article name in the collection

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

ISBN

978-3-95977-258-7

ISSN

1868-8969

e-ISSN

—

Number of pages

15

Pages from-to

1-15

Publisher name

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl

Event location

Seoul, Korea

Event date

Dec 19, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

—