The Ramsey number for stripes

Abstract

If G1,…,Gc are graphs without loops or multiple edges there is a smallest integer r(G1,…,Gc) such that if the edges of a complete graph Kn, with n ≧ r(G1,…,Gc), are painted arbitrarily with c colours the ith coloured subgraph contains Gi as a subgraph for at least one i. r(G1,…Gc) is called the Ramsey number of the graphs G1,…,Gc.

Three-Color Ramsey Numbers For Paths

“…Theorem 2 (Cockayne and Lorimer, 1975, [4]). Assume that n 1 ,... , n t ≥ 1 are integers and n 1 = max(n 1 ,... ,n t ).…”

More on monochromatic-rainbow Ramsey type theorems

“…We know that r(T n , 2) = n and r(nK 2 , 2) = 3n − 1. Generalizations of these two results appear in [1,[3][4][5]. For the related research see [6] and [7].…”

Ramsey-nice families of graphs

“…Extending a result of Cockayne and Lorimer [16] regarding the Ramsey number of matchings, Bialostocki and Gyárfás [9] proved that, for every positive integer k, the k-tuple (M 1 , . .…”