Maker-Breaker domination game critical graphs

Divakaran, Athira; Dravec, Tanja; James, Tijo; Klavžar, Sandi; Nair, Latha S.

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Title:	Maker-Breaker domination game critical graphs
Authors:	ID Divakaran, Athira (Author) ID Dravec, Tanja (Author) ID James, Tijo (Author) ID Klavžar, Sandi (Author) ID Nair, Latha S. (Author)
Files:	RAZ_Divakaran_Athira_2025.pdf (540,67 KB) MD5: 30FE7E963CD0C7B747F92AA834DA7D5C https://doi.org/10.1016/j.dam.2025.02.038
Language:	English
Work type:	Scientific work
Typology:	1.01 - Original Scientific Article
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	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.
Keywords:	Maker-Breaker game, Maker-Breaker domination game, Maker-Breaker domination number, Maker-Breaker domination game critical graph
Publication status:	Published
Publication version:	Version of Record
Submitted for review:	31.08.2024
Article acceptance date:	20.02.2025
Publication date:	28.02.2025
Year of publishing:	2025
Number of pages:	str. 126-134
Numbering:	Letn. 368
PID:	20.500.12556/DKUM-93911
UDC:	519.17
ISSN on article:	0166-218X
COBISS.SI-ID:	227767299
DOI:	10.1016/j.dam.2025.02.038
Publication date in DKUM:	25.07.2025
Views:	135
Downloads:	6
Metadata:
Categories:	Misc.
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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

Document is financed by a project

Funder:	ARIS - Slovenian Research and Innovation Agency
Project number:	P1-0297-2022
Name:	Teorija grafov

Funder:	ARIS - Slovenian Research and Innovation Agency
Project number:	N1-0285-2023
Name:	Metrični problemi v grafih in hipergrafih

Funder:	ARIS - Slovenian Research and Innovation Agency
Project number:	N1-0355-2024
Name:	Prirejanja, transverzale in hipergrafi

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.
Licensing start date:	28.02.2025

Secondary language

Language:	Slovenian
Title:	Kritični grafi za dominacijsko igro izdelovalec-lomilec
Abstract:	Dominacijska igra izdelovalec-lomilec (igra MBD) je igra za dva igralca, ki jo na grafu ▫$G$▫ igrata Dominator in Zavlačevalka. Igralca izmenično izbirata neizbrana vozlišča grafa ▫$G$▫. Cilj Dominatorja je, da z množico vozlišč, ki jih je izbral, tvori dominantno množico, medtem ko je cilj Zavlačevalke, da to prepreči. V tem članku preučujemo kritične grafe igre MBD. Ugotovljen je njihov obstoj in kritični grafi so opisani za večino primerov, v katerih lahko prvi igralec zmaga igro v eni ali dveh potezah.
Keywords:	dominacijska igra izdelovalec-lomilec, igra izdelovalec-lomilec, dominacijsko število izdelovalec-lomilec, kritični grafi za dominacijsko igro izdelovalec-lomilec

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