20.500.12556/DiRROS-28765 Builder-Blocker mutual-visibility game 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. mutual-visibility set games on graphs complete multipartite graph Hamming graph množica vzajemne vidnosti igre na grafih polni multipartitni graf Hammingov graf true false true Angleški jezik Slovenski jezik Neznano 2026-04-02 13:53:25 2026-04-02 13:53:26 2026-04-03 03:46:28 0000-00-00 00:00:00 2026 0 0 13 str. iss. 2, article no. 89 Vol. 49 Apr. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-04-01 519.17 0126-6705 10.1007/s40840-026-02083-9 274047747 s40840-026-02083-9.pdf s40840-026-02083-9.pdf 1 F3956BDA7BEB2D6FCC73E2E2873B3940 f85619cbe621b921770fe7297fbbeb6e29bc8597ddda25a2539a090655abfd87 43a7af03-2e8b-11f1-af78-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=42824 https://link.springer.com/article/10.1007/s40840-026-02083-9 1 92319bfa-2e8a-11f1-af78-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=42823 Inštitut za matematiko, fiziko in mehaniko 0 0 0