Builder-Blocker Mutual-Visibility Game

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Chenoweth V. I., Klavžar S., Rus G., TAN E., Tian J.

Bulletin of the Malaysian Mathematical Sciences Society, vol.49, no.2, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2026
  • Doi Number: 10.1007/s40840-026-02083-9
  • Journal Name: Bulletin of the Malaysian Mathematical Sciences Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Complete multipartite graph, Games on graphs, Hamming graph, Mutual-visibility set
  • Ankara University Affiliated: Yes

Abstract

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.