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Isomorphism Problem for Sd-Graphs

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AGAOGLU Deniz HLINĚNÝ Petr

Rok publikování 2020
Druh Článek ve sborníku
Konference 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.4230/LIPIcs.MFCS.2020.4
Klíčová slova intersection graph; isomorphism testing; interval graph; H-graph
Popis An H-graph is the intersection graph of connected subgraphs of a suitable subdivision of a fixed graph H, introduced by Biró, Hujter and Tuza (1992). We focus on S_d-graphs as a special case generalizing interval graphs. A graph G is an S_d-graph iff it is the intersection graph of connected subgraphs of a subdivision of a star S_d with d rays. We give an FPT algorithm to solve the isomorphism problem for S_d-graphs with the parameter d. This solves an open problem of Chaplick, Töpfer, Voborník and Zeman (2016). In the course of our proof, we also show that the isomorphism problem of S_d-graphs is computationally at least as hard as the isomorphism problem of posets of bounded width.
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