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...
A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G ...
Let D be a set of positive integers. The distance graph generated by D, denoted by G(Z, D), has the set Z of all integers as the vertex Supported in part by the National Science ...
An acyclic coloring of a graph G is a proper coloring of the vertex set of G such that G contains no bichromatic cycles. The acyclic chromatic number of a graph G is the minimum nu...
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....