Game domination number

Noga Alon, József Balogh, Béla Bollobás, Tamás Szabó
2002 Discrete Mathematics  
The game domination number of a (simple, undirected) graph is deÿned by the following game. Two players, A and D, orient the edges of the graph alternately until all edges are oriented. Player D starts the game, and his goal is to decrease the domination number of the resulting digraph, while A is trying to increase it. The game domination number of the graph G, denoted by g(G), is the domination number of the directed graph resulting from this game. This is well deÿned if we suppose that both
more » ... layers follow their optimal strategies. We determine the game domination number for several classes of graphs and provide general inequalities relating it to other graph parameters.
doi:10.1016/s0012-365x(00)00358-7 fatcat:b7ayobluunac5d77h7lpo4spbm