Star-path bipartite Ramsey numbers

For bipartite graphs G1, G2, …, Gk, the bipartite Ramsey number b(G1, G2, …, Gk) is the least positive integer b so that any colouring of the edges of Kb,b with k colours will result in a copy of Gi in the ith colour for some i. In this note, we establish the exact value of the bipartite Ramsey number b(Pm, Kl,n) for all integers m, n ⩾ 2, where Pm denotes a path on m vertices.