Maker-Breaker domination number - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin of the Malaysian Mathematical Sciences Society Année : 2019

Maker-Breaker domination number

Résumé

The Maker-Breaker domination game is played on a graph G by Dominator and Staller. The players alternatively select a vertex of G that was not yet chosen in the course of the game. Dominator wins if at some point the vertices he has chosen form a dominating set. Staller wins if Dominator cannot form a dominating set. In this paper we introduce the Maker-Breaker domination number γ MB (G) of G as the minimum number of moves of Dominator to win the game provided that he has a winning strategy and is the first to play. If Staller plays first, then the corresponding invariant is denoted γ MB (G). Comparing the two invariants it turns out that they behave much differently than the related game domination numbers. The invariant γ MB (G) is also compared with the domination number. Using the Erd˝ os-Selfridge Criterion a large class of graphs G is found for which γ MB (G) > γ(G) holds. Residual graphs are introduced and used to bound/determine γ MB (G) and γ MB (G). Using residual graphs, γ MB (T) and γ MB (T) are determined for an arbitrary tree. The invariants are also obtained for cycles and bounded for union of graphs. A list of open problems and directions for further investigations is given.
Fichier principal
Vignette du fichier
MB-number-submit.pdf (282.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01935244 , version 1 (26-11-2018)

Identifiants

Citer

Valentin Gledel, Vesna Iršič, Sandi Klavžar. Maker-Breaker domination number. Bulletin of the Malaysian Mathematical Sciences Society, 2019, ⟨10.1007/s40840-019-00757-1⟩. ⟨hal-01935244⟩
93 Consultations
122 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More