Generalizing the Ramsey Problem through Diameter
Generalizing the Ramsey Problem through Diameter
Given a graph $G$ and positive integers $d,k$, let $f_d^k(G)$ be the maximum $t$ such that every $k$-coloring of $E(G)$ yields a monochromatic subgraph with diameter at most $d$ on at least $t$ vertices. Determining $f_1^k(K_n)$ is equivalent to determining classical Ramsey numbers for multicolorings. Our results include $\bullet$ determining …