Gallai–Ramsey Numbers for a Class of Graphs with Five Vertices

Xihe Li, Ligong Wang

科研成果: 期刊稿件文章同行评审

9 引用 (Scopus)

摘要

Given two graphs G and H, the k-colored Gallai–Ramsey number grk(G: H) is defined to be the minimum integer n such that every k-coloring of the complete graph on n vertices contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we consider grk(K3: H) , where H is a connected graph with five vertices and at most six edges. There are in total thirteen graphs in this graph class, and the Gallai–Ramsey numbers for eight of them have been studied step by step in several papers. We determine all the Gallai–Ramsey numbers for the remaining five graphs, and we also obtain some related results for a class of unicyclic graphs. As applications, we find the mixed Ramsey spectra S(n; H, K3) for these graphs by using the Gallai–Ramsey numbers.

源语言英语
页(从-至)1603-1618
页数16
期刊Graphs and Combinatorics
36
6
DOI
出版状态已出版 - 1 11月 2020

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