2023/02/20 by Mao, Yaping
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2302.10770
Given two graphs G and H, the general k-colored Gallai-Ramsey number grk(G:H) is defined to be the minimum integer m such that every k-coloring of the complete graph on m vertices contains either a rainbow copy of G or a monochromatic copy of H. Interesting problems arise when one asks how many such rainbow copy of G and monochromatic copy of H must occur. The Gallai-Ramsey multiplicity GMk(G,H) is defined as the minimum total number of rainbow copy of G and monochromatic copy of H in any exact k-coloring of K_grk(G,H). In this paper, we give upper and lower bounds for Gallai-Ramsey multiplicity involving some small rainbow subgraphs.