Builder-Blocker mutual-visibility game

Iršič Chenoweth, Vesna (author), Klavžar, Sandi (author), Rus, Gregor (author), Tan, Elif (author), Tian, Jing (author)

This article discusses mutual-visibility in graphs through a game-based version of the problem. Two players, Builder and Blocker, alternately select an unmarked vertex on a graph keeping the property that the set of marked vertices forms a mutual-visibility set. The game ends when no such selection is possible. The goal of Builder is to create a largest possible mutual-visibility set, Blocker's goal is the opposite. The central problem here is to determine the number of vertices selected during the game assuming that both players played optimally. Bounds on this number are proved and several general properties of the game derived. Special attention is paid to complete multipartite graphs and Hamming graphs.

• Language: English
• Keywords: mutual-visibility set, games on graphs, complete multipartite graph, Hamming 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
• Publication date: 01.04.2026
• Year: 2026
• Number of pages: 13 str.
• Numbering: Vol. 49, iss. 2, article no. 89
• PID: 20.500.12556/RUL-181356
• UDC: 519.17
• ISSN on article: 0126-6705
• DOI: 10.1007/s40840-026-02083-9
• COBISS.SI-ID: 274047747
• Publication date in RUL: 02.04.2026

Record is a part of a journal

• Title: Bulletin of the Malaysian Mathematical Sciences Society
• Shortened title: Bull. Malays. Math. Sci. Soc.
• Publisher: Malaysian Mathematical Society, Springer
• ISSN: 0126-6705
• COBISS.SI-ID: 515781657

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: množica vzajemne vidnosti, igre na grafih, polni multipartitni graf, Hammingov graf