Characterization of edge-colored complete graphs with properly colored Hamilton paths

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Characterization of edge-colored complete graphs with properly colored Hamilton paths

An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edgecolored complete graph G has a properly colored Hamilton path if and only if G has a spanning subgraph consisting of a properly colored path C0 and a (possibly empty) collection of properly colored cycles C1, C2, . . . , Cd such that V (Ci) ...

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Properly colored Hamilton cycles in edge-colored complete graphs

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Long properly colored cycles in edge colored complete graphs

Let Kc n denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(Kc n) denote the maximum number of edges of the same color incident with a vertex of Kn. A properly colored cycle (path) in Kc n is a cycle (path) in which adjacent edges have distinct colors. B. Bollobás and P. Erdös (1976) proposed the following conjecture: If ∆mon(Kc n) < b 2 c, then Kc n con...

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ژورنال

عنوان ژورنال: Journal of Graph Theory

سال: 2006

ISSN: 0364-9024,1097-0118

DOI: 10.1002/jgt.20188