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In the domination game studied here, Dominator and Staller alternately choose a vertex of a graph G and take it into a set D. The number of vertices dominated by the set D must increase in each single turn and the game ends when D becomes a dominating set of G. Dominator aims to minimize whilst Staller aims to maximize the number of turns (or equivalently,… (More)

In the domination game, introduced by Brešar, Klavžar, and Rall in 2010, Dom-inator and Staller alternately select a vertex of a graph G. A move is legal if the selected vertex v dominates at least one new vertex – that is, if we have a u ∈ N [v] for which no vertex from N [u] was chosen up to this point of the game. The game ends when no more legal moves… (More)

The domination number γ(H) and the transversal number τ (H) (also called vertex covering number) of a hypergraph H are defined analogously to those of a graph. A hypergraph is of rank k if each edge contains at most k vertices. The inequality τ (H) ≥ γ(H) is valid for every hypergraph H without isolated vertices. We study the structure of hypergraphs… (More)