A note on Gallai-Ramsey number of even wheels
A note on Gallai-Ramsey number of even wheels
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DOI：
10.1016/j.disc.2019.111725
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Zi-Xia Song;B. Wei;Fangfang Zhang;Qing-Qing Zhao-Qing
中科院分区：
文献类型：
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作者：
Zi-Xia Song;B. Wei;Fangfang Zhang;Qing-Qing Zhao-Qing
完全图的Gallai染色是一种边染色，使得没有三角形的所有边都是不同的颜色。Gallai k-着色是使用k种颜色的Gallai着色。给定一个图H和一个整数k≥ 1，H的Gallai-Ramsey数GRk（H）是使得完全图KN的每一个Gallaik-染色都包含H的单色副本的最小正整数N.设W n表示n+ 1个顶点上的轮.本文研究了W2 n的Gallai-Ramsey数，并完全确定了当k≥ 2时GRk（W 4）的精确值.
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 G R 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 2 n and completely determine the exact value of G R k (W 4) for all k≥ 2.