Abstract
Given a graph G and a positive integer k, the 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 the sharp values for all m≤5.
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