126 research outputs found
Proper Hamiltonian Cycles in Edge-Colored Multigraphs
A -edge-colored multigraph has each edge colored with one of the
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
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]
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