We investigate the minimization problem of the minimum degree of minimal Ramsey graphs, initiated by Burr, Erd˝os, and Lov´asz. We determine the corresponding graph parameter fo...
In the online F-avoidance edge-coloring game with r colors, a graph on n vertices is generated by at each stage randomly adding a new edge. The player must color each new edge as ...
Given a graph on n vertices which is the union of two comparability graphs on the same vertex set, it always contains a clique or independent set of size n 1 3 . On the other hand...
The vertex Folkman number F(r, n, m), n < m, is the smallest integer t such that there exists a Km-free graph of order t with the property that every r-coloring of its vertices...
In this paper we bring together the areas of combinatorics and propositional satisfiability. Many combinatorial theorems establish, often constructively, the existence of positive...
Michael R. Dransfield, Lengning Liu, Victor W. Mar...