REAL

The variety of domination games

Brešar, B. and Bujtás, Csilla and Gologranc, T. and Klavžar, S. and Košmrlj, G. and Patkós, Balázs and Tuza, Zsolt and Vizer, Máté (2019) The variety of domination games. AEQUATIONES MATHEMATICAE, First. ISSN 0001-9054

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Abstract

Domination game (Brešar et al. in SIAM J Discrete Math 24:979–991, 2010) and total domination game (Henning et al. in Graphs Comb 31:1453–1462 (2015) are by now well established games played on graphs by two players, named Dominator and Staller. In this paper, Z-domination game, L-domination game, and LL-domination game are introduced as natural companions of the standard domination games. Versions of the Continuation Principle are proved for the new games. It is proved that in each of these games the outcome of the game, which is a corresponding graph invariant, differs by at most one depending whether Dominator or Staller starts the game. The hierarchy of the five domination games is established. The invariants are also bounded with respect to the (total) domination number and to the order of a graph. Values of the three new invariants are determined for paths up to a small constant independent from the length of a path. Several open problems and a conjecture are listed. The latter asserts that the L-domination game number is not greater than 6 / 7 of the order of a graph. © 2019, Springer Nature Switzerland AG.

Item Type: Article
Uncontrolled Keywords: Domination game; total domination game; Grundy domination number; L-domination game; Z-domination game;
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 23 Oct 2019 05:27
Last Modified: 20 Apr 2023 09:23
URI: http://real.mtak.hu/id/eprint/102585

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