1 9 N ov 2 01 4 The Disjoint Domination Game ∗
نویسندگان
چکیده
We introduce and study a Maker-Breaker type game in which the issue is to create or avoid two disjoint dominating sets in graphs without isolated vertices. We prove that the maker has a winning strategy on all connected graphs if the game is started by the breaker. This implies the same in the (2 : 1) biased game also in the maker-start game. It remains open to characterize the maker-win graphs in the maker-start non-biased game, and to analyze the (a : b) biased game for (a : b) 6= (2 : 1). For a more restricted variant of the non-biased game we prove that the maker can win on every graph without isolated vertices.
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