Ramsey upper density of infinite graphs

Abstract For a fixed infinite graph $H$ , we study the largest density of monochromatic subgraph isomorphic to that can be found in every two-colouring edges $K_{\mathbb{N}}$ . This is called Ramsey upper and was introduced by Erdős Galvin restricted setting, DeBiasio McKenney general. Recently [4], path determined. Here, find value this for all locally finite graphs up factor 2, answering question McKenney. We also exact wide class bipartite graphs, including forests. Our approach relates problem solution an optimisation continuous functions. show that, under certain conditions, depends only on chromatic number components expansion ratio $|N(I)|/|I|$ independent sets