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arXiv · 2008.09294

Properly colored cycles in edge-colored complete graphs containing no monochromatic triangles: a vertex-pancyclic analogous result

Ruonan Li
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Abstract

A properly colored cycle (path) in an edge-colored graph is a cycle (path) with consecutive edges assigned distinct colors. A monochromatic triangle is a cycle of length $3$ with the edges assigned a same color. It is known that every edge-colored complete graph without containing monochromatic triangles always contains a properly colored Hamilton path. In this paper, we investigate the existence of properly colored cycles in edge-colored complete graphs when monochromatic triangles are forbidden. We obtain a vertex-pancyclic analogous result combined with a characterization of all the exceptions.

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Ruonan Li. 2020-08-21. Properly colored cycles in edge-colored complete graphs containing no monochromatic triangles: a vertex-pancyclic analogous result. https://arxiv.org/abs/2008.09294

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