Improved bounds for anti-Ramsey numbers of matchings in outerplanar graphs

DOI10.1016/J.AMC.2021.126843arXiv2005.08169MaRDI QIDQ6340858

Hua He, Yongxin Lan, Yifan Pei

Publication date: 17 May 2020

Abstract: Let $mathcal{O}_n$ be the set of all maximal outerplanar graphs of order $n$. Let $ar(mathcal{O}_n,F)$ denote the maximum positive integer $k$ such that $Tinmathcal{O}_n$ has no rainbow subgraph $F$ under a $k$-edge-coloring of $T$. Denote by $M_k$ a matching of size $k$. In this paper, we prove that $ar(mathcal{O}_n,M_k)len+4k-9$ for $nge3k-3$, which expressively improves the existing upper bound for $ar(mathcal{O}_n,M_k)$. We also prove that $ar(mathcal{O}_n,M_5)=n+4$ for all $nge15$.

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Coloring of graphs and hypergraphs (05C15) Generalized Ramsey theory (05C55) Ramsey theory (05D10)

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