Upper density of monochromatic paths in edge-coloured infinite complete graphs and bipartite graphs

A. Nicholas Day, Allan Lo

The upper density of an infinite graph $G$ with $V(G)\subseteq \mathbb{N}$ is defined as $\overline{d}(G)={\mathrm{limsup}}_{n\to \infty }|V(G)\cap \{1,\dots ,n\}|/n$. Let $K…