The Disjoint Domination Game

Abstract

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)≠(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. © 2015 Elsevier B.V