Tiling with monochromatic bipartite graphs of bounded maximum degree - Girao, Antonio; Janzer, Oliver (Arxiv, 2021)
We prove that for any r∈N, there exists a constant Cr such that the following is true. Let F={F1,F2,…} be an infinite sequence of bipartite graphs such that |V(Fi)|=i and Δ(Fi)≤Δ hold for all i. Then in any r-edge coloured complete graph Kn, there is a collection of at most exp(CrΔ) monochromatic subgraphs, each of which is isomorphic to an element of F, whose vertex sets partition V(Kn). This proves a conjecture of Corsten and Mendonça in a strong form and generalizes results on the multicolour Ramsey numbers of bounded-degree bipartite graphs.