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The Hamiltonian Cycle Problem and Monotone Classes

Published: 01 July 2024 Publication History
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  • Abstract

    We study the computational complexity of the Hamiltonian cycle problem on monotone classes of graphs, i.e. classes closed under taking subgraphs. We focus on classes defined by a single forbidden subgraph and present some necessary and some sufficient conditions for polynomial-time solvability of the problem in this case (assuming PNP). The main result is a polynomial-time algorithm to solve the problem for graphs excluding a certain tree, called the long-H, as a subgraph.

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    Published In

    cover image Guide Proceedings
    Combinatorial Algorithms: 35th International Workshop, IWOCA 2024, Ischia, Italy, July 1–3, 2024, Proceedings
    Jul 2024
    556 pages
    ISBN:978-3-031-63020-0
    DOI:10.1007/978-3-031-63021-7
    • Editors:
    • Adele Anna Rescigno,
    • Ugo Vaccaro

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    Springer-Verlag

    Berlin, Heidelberg

    Publication History

    Published: 01 July 2024

    Author Tags

    1. Hamiltonian cycle
    2. Polynomial algorithm
    3. Monotone class

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