2018/09/26 by Zhao Wang, Wang, Zhao, Yaping Mao +5 · 3 citations
Mathematics · #05C55 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C55
paper · pdf · doi:10.48550/arxiv.1809.10298
17 pages. arXiv admin note: text overlap with arXiv:1802.04930
arxiv created 2018/09/26 · arxiv updated 2018/09/28
Given a graph G and a positive integer k, define the Gallai-Ramsey number 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 consider two classes of unicyclic graphs, the star with an extra edge and the path with a triangle at one end. We provide the 2-color Ramsey numbers for these two classes of graphs and use these to obtain general upper and lower bounds on the Gallai-Ramsey numbers.