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

DOI10.1016/J.DISC.2021.112573arXiv2008.09294MaRDI QIDQ6347477

Publication date: 20 August 2020

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.

Mathematics Subject Classification ID

Paths and cycles (05C38) Coloring of graphs and hypergraphs (05C15) Graph algorithms (graph-theoretic aspects) (05C85)

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