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Counting Traversing Hamiltonian Cycles in Tiled Graphs

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  • Alen Vegi Kalamar

    (Department of Mathematics and Computer Science, University of Maribor, 2000 Maribor, Slovenia
    Comtrade Gaming, 2000 Maribor, Slovenia)

Abstract

Recently, the problem of counting Hamiltonian cycles in 2-tiled graphs was resolved by Vegi Kalamar, Bokal, and Žerak. In this paper, we continue our research on generalized tiled graphs. We extend algorithms on counting traversing Hamiltonian cycles from 2-tiled graphs to generalized tiled graphs. We further show that, similarly as for 2-tiled graphs, for a fixed finite set of tiles, counting traversing Hamiltonian cycles can be performed in linear time with respect to the size of such graph, implying that counting traversing Hamiltonian cycles in tiled graphs is fixed-parameter tractable.

Suggested Citation

  • Alen Vegi Kalamar, 2023. "Counting Traversing Hamiltonian Cycles in Tiled Graphs," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2650-:d:1168143
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    References listed on IDEAS

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    1. Jelena Đokić & Ksenija Doroslovački & Olga Bodroža-Pantić, 2023. "A Spanning Union of Cycles in Thin Cylinder, Torus and Klein Bottle Grid Graphs," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
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