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 Kn 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 Bm=K2+Km and prove sharp results for m≤5.
@article{arxiv.1802.04930,
title = {Gallai-Ramsey numbers for books},
author = {Jinyu Zou and Yaping Mao and Colton Magnant and Zhao Wang and Chengfu Ye},
journal= {arXiv preprint arXiv:1802.04930},
year = {2018}
}