2017/07/21 by Khoeini, Farideh, Dzido, Tomasz
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.06955
For given graphs G1, G2, ... , Gk, k ≥ 2, the multicolor Ramsey number R(G1, G2, ... , Gk) is the smallest integer n such that if we arbitrarily color the edges of the complete graph of order n with k colors, then it always contains a monochromatic copy of Gi colored with i, for some 1 ≤ i ≤ k. The bipartite Ramsey number b(G1, ⋯, Gk) is the least positive integer b such that any coloring of the edges of Kb,b with k colors will result in a monochromatic copy of bipartite Gi in the i-th color, for some i, 1 ≤ i ≤ k. There is very little known about R(G1,…, Gk) even for very special graphs, there are a lot of open cases. In this paper, by using bipartite Ramsey numbers we obtain the exact values of some multicolor Ramsey numbers. We show that for sufficiently large n0 and three following cases: 1. n1=2s, n2=2m and m-1<2s, 2. n1=n2=2s, 3. n1=2s+1, n2=2m and s