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arXiv · 1903.10319

Anti-Ramsey numbers of graphs with some decomposition family sequences

Long-Tu Yuan·Xiao-Dong Zhang
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Abstract

For a given graph $H$, the anti-Ramsey number of $H$ is the maximum number of colors in an edge-coloring of a complete graph which does not contain a rainbow copy of $H$. In this paper, we extend the decomposition family of graphs to the decomposition family sequence of graphs and show that $K_5$ is determined by its decomposition family sequence. Based on this new graph notation, we determine the anti-Ramsey numbers for new families of graphs, including the Petersen graph, vertex-disjoint union of cliques, etc., and characterize the extremal colorings.

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Long-Tu Yuan, Xiao-Dong Zhang. 2019-03-25. Anti-Ramsey numbers of graphs with some decomposition family sequences. https://arxiv.org/abs/1903.10319

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