Other formats:
BibTeX
LaTeX
RIS
@article{2218880,
author = {Agaoglu Cagirici, Deniz and Hliněný, Petr},
article_location = {UNITED STATES},
article_number = {2},
doi = {http://dx.doi.org/10.1007/s00453-022-01033-8},
keywords = {intersection graph; isomorphism testing; chordal graph; H-graph; parameterized complexity},
language = {eng},
issn = {0178-4617},
journal = {ALGORITHMICA},
title = {Efficient Isomorphism for Sd-Graphs and T-Graphs},
url = {http://arxiv.org/abs/1907.01495},
volume = {85},
year = {2023}
}
TY - JOUR
ID - 2218880
AU - Agaoglu Cagirici, Deniz - Hliněný, Petr
PY - 2023
TI - Efficient Isomorphism for Sd-Graphs and T-Graphs
JF - ALGORITHMICA
VL - 85
IS - 2
SP - 352-383
EP - 352-383
PB - SPRINGER
SN - 01784617
KW - intersection graph
KW - isomorphism testing
KW - chordal graph
KW - H-graph
KW - parameterized complexity
UR - http://arxiv.org/abs/1907.01495
N2 - 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.
ER -
AGAOGLU CAGIRICI, Deniz and Petr HLINĚNÝ. Efficient Isomorphism for Sd-Graphs and T-Graphs. \textit{ALGORITHMICA}. UNITED STATES: SPRINGER, 2023, vol.~85, No~2, p.~352-383. ISSN~0178-4617. Available from: https://dx.doi.org/10.1007/s00453-022-01033-8.
|
