paper

Gallai-Ramsey numbers for books

arXiv:1802.04930

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 $B_{m} = K_{2} + K_{m}$ and prove sharp results for $m \leq 5$ .

24 pages, 4 figures