Abstract
AbstractWe consider the graph coloring game, a game in which two players take turns properly coloring the vertices of a graph, with one player attempting to complete a proper coloring, and the other player attempting to prevent a proper coloring. We show that if a graph has a proper coloring in which the game coloring number of each bicolored subgraph is bounded, then the game chromatic number of is bounded. As a corollary to this result, we show that for two graphs and with bounded game coloring number, the Cartesian product has bounded game chromatic number, answering a question of X. Zhu. We also obtain an upper bound on the game chromatic number of the strong product of two graphs.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
