Year: 2026
Type: article
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.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G1414015028, G1632905356, Matchings, transversals, and hypergraphs, G1921315438, Domination in graphs: cubic graphs, products and games, Graph theory, G5099342464, Metric Problems in Graphs and Hypergraphs, The game of Cops and Robber on graphs and geodesic spaces, G7056179351, General Position and Visibility in Graph Theory, G8106254168
OpenAlex ID: W7147352202