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 $(a:b)\ne (2:1)$. For a more restricted variant of the non-biased game we prove that the maker can win on every graph without isolated vertices.

18 pages

References in corpus (2)

• Domination game played on trees and spanning subgraphs
• On the game domination number of graphs with given minimum degree