Efficient Isomorphism for Sd-Graphs and T-Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F23%3A00130021" target="_blank" >RIV/00216224:14330/23:00130021 - isvavai.cz</a>

Result on the web

<a href="http://arxiv.org/abs/1907.01495" target="_blank" >http://arxiv.org/abs/1907.01495</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00453-022-01033-8" target="_blank" >10.1007/s00453-022-01033-8</a>

Result language

angličtina

Original language name

Efficient Isomorphism for Sd-Graphs and T-Graphs

Original language description

An H-graph is one representable as the intersection graph of connected subgraphs of a suitable subdivision of a fixed graph H, introduced by Biró et al. (Discrete Mathematics 100:267–279, 1992). An H-graph is proper if the representing subgraphs of H can be chosen incomparable by the inclusion. In this paper, we focus on the isomorphism problem for Sd-graphs and T-graphs, where Sd is the star with d rays and T is an arbitrary fixed tree. Answering an open problem of Chaplick et al. (2016, personal communication), we provide an FPT-time algorithm for testing isomorphism and computing the automorphism group of Sd-graphs when parameterized by d, which involves the classical group-computing machinery by Furst et al. (in Proceedings of 11th southeastern conference on combinatorics, graph theory, and computing, congressum numerantium 3, 1980). We also show that the isomorphism problem of Sd-graphs is at least as hard as the isomorphism problem of posets of bounded width, for which no efficient combinatorial-only algorithm is known to date. Then we extend our approach to an XP-time algorithm for isomorphism of T-graphs when parameterized by the size of T. Lastly, we contribute an FPT-time combinatorial algorithm for isomorphism testing in the special case of proper Sd- and T-graphs.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10200 - Computer and information sciences

Project

<a href="/en/project/GA20-04567S" target="_blank" >GA20-04567S: Structure of tractable instances of hard algorithmic problems on graphs</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2023

Confidentiality

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

Name of the periodical

ALGORITHMICA

ISSN

0178-4617

e-ISSN

1432-0541

Volume of the periodical

85

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

32

Pages from-to

352-383

UT code for WoS article

000850021200002

EID of the result in the Scopus database

2-s2.0-85137458099