2018/11/15 by Xihe Li, Li, Xihe, Ligong Wang +1
Computer Science · Mathematics · #05C15 #05C55 #05D10 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1811.06134
openalex publication_date 2018/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 some of them have been studied step by step in several papers. We determine all the Gallai-Ramsey numbers for the remaining graphs, and we also obtain some related results for a class of unicyclic graphs.