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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)
Three edges e 1 , e 2 and e 3 in a graph G are consecutive if they form a path (in this order) or a cycle of length 3. The 3-consecutive edge coloring number ψ 3c (G) of G is the maximum number of colors permitted in a coloring of the edges of G such that if e 1 , e 2 and e 3 are consecutive edges in G, then e 1 or e 3 receives the color of e 2. Here we(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)