The Disjoint Domination Game

Csilla Bujtás, Z. Tuza

Research output: Contribution to journalArticle

12 Citations (Scopus)

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.

Original languageEnglish
JournalDiscrete Mathematics
DOIs
Publication statusAccepted/In press - Nov 19 2014

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Domination
Disjoint
Game
Biased
Graph in graph theory
Dominating Set
Connected graph
Imply

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

The Disjoint Domination Game. / Bujtás, Csilla; Tuza, Z.

In: Discrete Mathematics, 19.11.2014.

Research output: Contribution to journalArticle

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