More results on the complexity of domination problems in graphs
by Olivier Hudry; Antoine Lobstein
International Journal of Information and Coding Theory (IJICOT), Vol. 4, No. 2/3, 2017

Abstract: Given a graph G = (V, E) and an integer r ≥ 1, we call 'r-dominating code' any subset C of V such that every vertex in V is at distance at most r from at least one vertex in C. We investigate and locate in the complexity classes of the polynomial hierarchy, several problems linked with domination in graphs, such as, given r and G, the existence of, or search for, optimal r-dominating codes in G, or optimal r-dominating codes in G containing a subset of vertices X ⊂ V .

Online publication date: Mon, 24-Apr-2017

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