Maker–Breaker domination game critical graphs

Divakaran, Athira (author), Dravec, Tanja (author), James, Tijo (author), Klavžar, Sandi (author), Nair, Latha S. (author)

The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$. The goal of Dominator is to form a dominating set with the set of vertices selected by him while that of Staller is to prevent this from happening. In this paper MBD game critical graphs are studied. Their existence is established and critical graphs are characterized for most of the cases in which the first player can win the game in one or two moves.

• Language: English
• Keywords: Maker-Breaker game, Maker-Breaker domination game, Maker-Breaker domination number, Maker-Breaker domination game critical graph
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 126-134
• Numbering: Vol. 368
• PID: 20.500.12556/RUL-167809
• UDC: 519.17
• ISSN on article: 0166-218X
• DOI: 10.1016/j.dam.2025.02.038
• COBISS.SI-ID: 227767299
• Publication date in RUL: 13.03.2025

Record is a part of a journal

• Title: Discrete applied mathematics
• Shortened title: Discrete appl. math.
• Publisher: Elsevier
• ISSN: 0166-218X
• COBISS.SI-ID: 25342464

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: dominacijska igra izdelovalec-lomilec, igra izdelovalec-lomilec, dominacijsko število izdelovalec-lomilec, kritični grafi za dominacijsko igro izdelovalec-lomilec