The adaptable chromatic number of a graph G is the smallest integer k such that for any edge k-colouring of G there exists a vertex kcolouring of G in which the same colour never ...
The forcing number of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matching of G. In this paper, we demon...
This paper discusses the game colouring number of partial k-trees and planar graphs. Let colg(PT k) and colg(P) denote the maximum game colouring number of partial k trees and the...
—We give an inequality for the group chromatic number of a graph as an extension of Brooks’ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality...
We find exact values for the game chromatic number of the Cartesian product graphs Sm Pn, Sm Cn, P2 Wn, and P2 Km,n. This extends previous results of Bartnicki et al. on the game...