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arXiv · 1802.04930

Gallai-Ramsey numbers for books

Jinyu Zou·Yaping Mao·Colton Magnant·Zhao Wang·Chengfu Ye
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Abstract

Given a graph $G$ and a positive integer $k$, the \emph{Gallai-Ramsey number} is defined to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $G$. In this paper, we obtain general upper and lower bounds on the Gallai-Ramsey numbers for books $B_{m} = K_{2} + \overline{K_{m}}$ and prove sharp results for $m \leq 5$.

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Jinyu Zou, Yaping Mao, Colton Magnant, Zhao Wang, Chengfu Ye. 2018-02-14. Gallai-Ramsey numbers for books. https://arxiv.org/abs/1802.04930

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