Nordhaus-Gaddum Bounds for k-Domination in Graphs
نویسنده
چکیده
A k-dominating set of a graph G is a set S of vertices of G such that every vertex outside of S has k neighbors in S. The k-domination number of G, written γk(G), is the size of the smallest k-dominating set in G. In this paper, we derive sharp upper and lower bounds on γk(G) + γk(G) and γk(G)γk(G), where G is the complement of G. We use the results for k = 2 to prove a conjecture of Alon, Balogh, Bollobás, and Szabó on game domination numbers.
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