Improved bounds for anti-Ramsey numbers of matchings in outer-planar graphs

Yifan Pei, Yongxin Lan and Hua He

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: Let On be the set of all maximal outer-planar graphs of order n. Let ar(On,F) denote the maximum positive integer k such that there is a k-edge-coloring of a graph T in the family On which has no rainbow subgraph F. Denote by Mk a matching of size k. In this paper, we prove that ar(On,Mk)≤n+4k−9 for n≥3k−3, which expressively improves the existing upper bound for ar(On,Mk). We also prove that ar(On,M5)=n+4 for all n≥15.

Keywords: Anti-Ramsey number; Outer-planar graph; Matching (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009267

DOI: 10.1016/j.amc.2021.126843

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