Tiling with monochromatic bipartite graphs of bounded maximum degree

Abstract

Abstract We prove that for any , there exists a constant such that the following is true. Let be an infinite sequence of bipartite graphs such that and hold for all . Then, in any ‐edge‐coloured complete graph , there is a collection of at most monochromatic subgraphs, each of which is isomorphic to an element of , whose vertex sets partition . This proves a conjecture of Corsten and Mendonça in a strong form and generalises results on the multi‐colour Ramsey numbers of bounded‐degree bipartite graphs. It also settles the bipartite case of a general conjecture of Grinshpun and Sárközy.