Domination Game: Extremal Families for the 3/5-Conjecture for Forests

• Autorzy: Michael A. Henning , Christian Löwenstein
• Języki publikacji: EN

Abstrakty

EN

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) ≤ ⅗n 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) = ⅗n, then every component of G belongs to our construction.

Słowa kluczowe

EN

domination game; 3/5 conjecture

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 2
• Strony: 369-381

Daty

wydano

2017-05-01

otrzymano

2015-10-21

poprawiono

2016-04-30

zaakceptowano

2016-04-30

online

2017-04-01

Twórcy

autor

Michael A. Henning

• Department of Pure and Applied Mathematics University of Johannesburg Auckland Park, 2006,

autor

Christian Löwenstein

• Institute of Optimization and Operations Research Ulm University Ulm 89081,

Identyfikatory

DOI

10.7151/dmgt.1931