2020/05/17 by Pei, Yifan, Lan, Yongxin, He, Hua
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.08169
Let On be the set of all maximal outerplanar graphs of order n. Let ar(On,F) denote the maximum positive integer k such that T∈ On has no rainbow subgraph F under a k-edge-coloring of T. 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.