126 research outputs found

    Proper Hamiltonian Cycles in Edge-Colored Multigraphs

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    A cc-edge-colored multigraph has each edge colored with one of the cc available colors and no two parallel edges have the same color. A proper Hamiltonian cycle is a cycle containing all the vertices of the multigraph such that no two adjacent edges have the same color. In this work we establish sufficient conditions for a multigraph to have a proper Hamiltonian cycle, depending on several parameters such as the number of edges and the rainbow degree.Comment: 13 page

    Long rainbow cycles in proper edge-colorings of complete graphs

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    We show that any properly edge-colored Kn contains a rainbow cycle with at least (4=7 − o(1))n edges. This improves the lower bound of n=2 − 1 proved in [1]

    Properly colored and rainbow cycles in edge-colored graphs

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