On mixed Ramsey numbers (Q5917806)

For a graph-theoretic parameter \(f\), an integer \(m\) and a graph \(H\), the mixed Ramsey number \(v(f;m;H)\) is the least positive integer \(p\) such that if \(G\) is any graph of order \(p\), then either \(f(G) \geq m\) or \(\overline G\) contains a subgraph isomorphic to \(H\). The authors study mixed Ramsey numbers for vertex linear arboricity and other generalizations of chromatic number, such as the point partition number of \textit{D. R. Lick} and the reviewer [Can. J. Math. 22, 1082-1096 (1970; Zbl 0202.23502)], for graphs \(H\) such as complete graphs, claws, paths, and other trees. They also study the corresponding generalized mixed Ramsey number, where the edge set of the complete graph is partitioned into \(k \geq 2\) subsets.