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arXiv · 2109.13678

Gallai-Ramsey numbers involving a rainbow $4$-path

Jinyu Zou·Zhao Wang·Hong-Jian Lai·Yaping Mao
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Abstract

Given two non-empty graphs $G,H$ and a positive integer $k$, the Gallai-Ramsey number $\operatorname{gr}_k(G:H)$ is defined as the minimum integer $N$ such that for all $n\geq N$, every $k$-edge-coloring of $K_n$ contains either a rainbow colored copy of $G$ or a monochromatic copy of $H$. In this paper, we got some exact values or bounds for $\operatorname{gr}_k(P_5:H) \ (k\geq 3)$ if $H$ is a general graph or a star with extra independent edges or a pineapple.

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Jinyu Zou, Zhao Wang, Hong-Jian Lai, Yaping Mao. 2021-10-07. Gallai-Ramsey numbers involving a rainbow $4$-path. https://arxiv.org/abs/2109.13678

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