Efficient Isomorphism for Sd-Graphs and T-Graphs

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AGAOGLU CAGIRICI Deniz HLINĚNÝ Petr

Rok publikování 2022
Druh Článek v odborném periodiku
Časopis / Zdroj ALGORITHMICA
Fakulta / Pracoviště MU

Fakulta informatiky

Citace
Doi http://dx.doi.org/10.1007/s00453-022-01033-8
Klíčová slova intersection graph; isomorphism testing; chordal graph; H-graph; parameterized complexity
Popis 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.
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