Note on the three-coloured bipartite Ramsey numbers for paths. Issue 3 (3rd July 2021) - Wang, Ke; Zhou, Jiannan; He, Dong; Tong, Qinghe
Abstract : For bipartite graphs G 1, G 2, …, G k, the bipartite Ramsey number br ( G 1, G 2, …, G k ) is the least positive integer p so that any coloring of the edges of K p, p with k colors will result in a copy of G i in the i th color for some i . In this paper, we investigate the appearance of simpler monochromatic graphs such as paths under a 3-colouring of the edges of a bipartite graph. we obtain the exact value of br ( P 3, P 3, P n ), and br ( P 3, P 3, …, P n ) for n ≥ 4 r + 2, and br ( P 4, P 4, P n ) for n ≥ 4 by a new method of proof.