We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For kdegenerate graphs with...
The total chromatic number zt(G) of a graph G is the least number of colors needed to color the vertices and edges of G so that no adjacent vertices or edges receive the same colo...
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...
: Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player ...
This paper introduces a new strategy for playing the marking game on graphs. Using this strategy, we prove that if G is a planar graph, then the game colouring number of G, and he...