Elsevier

Discrete Mathematics

Volume 339, Issue 7, 6 July 2016, Pages 1985-1992
Discrete Mathematics

The Disjoint Domination Game

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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.

Keywords

Disjoint Domination Game
Dominating set
Games on graphs
Combinatorial game
Biased game

Cited by (0)

Research has been supported by the European Union and Hungary co-financed by the European Social Fund through the project TÁMOP-4.2.2.C-11/1/KONV-2012-0004–National Research Center for Development and Market Introduction of Advanced Information and Communication Technologies.