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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, Dominator 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)
Given an integer k ≥ 2, we consider vertex colorings of graphs in which no k-star subgraph Sk = K1,k is polychromatic. Equivalently, in a star-[k]-coloring the closed neighborhood N[v] of each vertex v can have at most k different colors on its vertices. The maximum number of colors that can be used in a star-[k]-coloring of graph G is denoted by χ̄k⋆(G)(More)
We consider vertex colorings of hypergraphs in which lower and upper bounds are prescribed for the largest cardinality of a monochromatic subset and/or of a polychromatic subset in each edge. One of the results states that for any integers s ≥ 2 and a ≥ 2 there exists an integer f (s, a)with the following property. If an interval hypergraph admits some(More)