Domination game: Extremal families for the 3/5-conjecture for forests

Michael A. Henning, Christian Löwenstein

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

In the domination game on a graph G, the players Dominator and Staller alternately select vertices of G. Each vertex chosen must strictly increase the number of vertices dominated. This process eventually produces a dominating set of G; Dominator aims to minimize the size of this set, while Staller aims to maximize it. The size of the dominating set produced under optimal play is the game domination number of G, denoted by γg(G). Kinnersley, West and Zamani [SIAM J. Discrete Math. 27 (2013) 2090-2107] posted their 3/5-Conjecture that γg(G) ≤ 3/5n for every isolate-free forest on n vertices. Brešar, Klavžar, Košmrlj and Rall [Discrete Appl. Math. 161 (2013) 1308-1316] presented a construction that yields an infinite family of trees that attain the conjectured 3/5-bound. In this paper, we provide a much larger, but simpler, construction of extremal trees. We conjecture that if G is an isolate-free forest on n vertices satisfying γg(G) = 3/5n, then every component of G belongs to our construction.

Original languageEnglish
Pages (from-to)369-381
Number of pages13
JournalDiscussiones Mathematicae - Graph Theory
Volume37
Issue number2
DOIs
Publication statusPublished - 2017

Keywords

  • 3/5-conjecture
  • Domination game

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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