Isomorphism Problem for S_d-Graphs

Authors Deniz Ağaoğlu , Petr Hliněný

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Deniz Ağaoğlu
  • Masaryk University, Brno, Czech Republic
Petr Hliněný
  • Masaryk University, Brno, Czech Republic


We would like to thank to Pascal Schweitzer for pointing us to the paper [Furst et al., 1980], and to Onur Çağırıcı for comments on this manuscript.

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Deniz Ağaoğlu and Petr Hliněný. Isomorphism Problem for S_d-Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • intersection graph
  • isomorphism testing
  • interval graph
  • H-graph


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