A note on Gallai-Ramsey number of even wheels

摘要

A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallai k-coloring is a Gallai coloring that uses k colors. Given a graph H and an integer k >= 1, the Gallai-Ramsey number GR(k)(H) of H is the least positive integer N such that every Gallai k-coloring of the complete graph K-N contains a monochromatic copy of H. Let W-n denote a wheel on n + 1 vertices. In this note, we study Gallai-Ramsey number of W-2n and completely determine the exact value of GR(k)(W-4) for all k >= 2. (C) 2019 Elsevier B.V. All rights reserved.