Department of Mathematics
In this paper we study three-color Ramsey numbers. Let K i,j denote a complete i by jbipartite graph. We shall show that (i) for any connected graphs G 1, G 2 and G 3, if r(G 1,G 2)≥s(G 3), then r(G 1, G 2, G 3)≥(r(G 1, G 2)−1)(χ(G 3)−1)+s(G 3), where s(G 3) is the chromatic surplus of G 3; (ii) (k+m−2)(n−1)+1≤r(K 1,k , K 1,m , K n )≤ (k+m−1)(n−1)+1, and ifk or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K k,m , K k,m , K n )≤c(n/logn), and r(C 2m , C 2m , K n )≤c(n/logn) m/(m−1) for sufficiently large n.
Monochromatic graph, Three-color Ramsey number
Source Publication Title
Graphs and Combinatorics
Link to Publisher's Edition
Shiu, W., Lam, P., & Li, Y. (2003). On some three-color Ramsey numbers. Graphs and Combinatorics, 19 (2). https://doi.org/10.1007/s00373-002-0495-7