Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γperfect if β(H) = Γ(H),...
One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a tr...
Determining the cardinality and describing the structure of H-free graphs is wellinvestigated for many graphs H. In the nineties, Prömel and Steger proved that for a graph H with...
Motivated by a problem that arises in the study of mirrored storage systems, we describe, for any fixed , > 0 and any integer d 2, explicit or randomized constructions of d-r...
Erdos proved that there are graphs with arbitrarily large girth and chromatic number. We study the extension of this for generalized chromatic numbers. Generalized graph coloring d...