Star-path bipartite Ramsey numbers

Three-colour bipartite Ramsey number $R_b(G_1,G_2,P_3)$

“…In [9], Hattingh and Henning have proved a recursive inequality [10]). Hattingh and Joubert calculated the number R b for pair of bistars (see [11]).…”

On size multipartite Ramsey numbers for stars

“…For simple graphs G and H, they defined the size multipartite Ramsey number m j (G, H) as the smallest natural number t such that any red-blue coloring on the edges of K j×t contains a red G or a blue H as a subgraph. The size bipartite Ramsey numbers for stars versus paths m 2 (K 1,m , P n ), for m, n ≥ 2 given by Hattingh and Henning [3]. In 2007, Syafrizal et al [11] determined the size multipartite Ramsey numbers for stars versus P 3 .…”

Bipartite Ramsey numbers involving stars, stripes and trees

“…In particular, research has been done to obtain exact values for small Ramsey numbers ( [1,8,12,17]). A first general upper bound was given by Irving [15] by exploring the similarity of the problem with Zarankiewicz's problem.…”

“…Subsequent work on general bounds for the problem was given by Thomason et al [22], by Hattingh et al [12], by Goddard et al [10], by Caro et al [4], by Conlon [6] and Lin et al [16]. Exact solutions were given for simpler cases of the problem such as path-path bipartite Ramsey numbers [9,11], star-star bipartite Ramsey numbers [17], star-path bipartite Ramsey numbers [13], K 2,2 -K 1,n and K 2,2 -K 2,n bipartite Ramsey numbers [2], C 2m -K 2,2 bipartite Ramsey numbers [21] and bipartite Ramsey numbers for multiple copies of K 2,2 [14]. Some variations of the bipartite case such as multicolour problems [3,5] and rainbow colouring problems [7] have been also studied.…”