Author: Patrick Dunn-Lawless
Dunn-Lawless, Patrick, 2023 Heuristic Algorithms in Maker-Breaker Secure Domination Games, Flinders University, College of Science and Engineering
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This thesis considers the Maker-Breaker domination game, a special case of Maker-Breaker games introduced in 2020. Since these games always have a theoretical winner, the majority of analysis in the literature has been towards identifying graphs where a specific player has a guaranteed winning strategy. However, little consideration has been given to how these games play out when a winning strategy is not known to either player. The Maker-Breaker domination game can be naturally extended by considering variants of dominating sets, and this thesis does so by considering secure dominating sets in a simulation environment. The results of these simulations are analysed to see which strategies are more successful. The strategies considered are based on various heuristics and results in the literature
Keywords: Maker-Breaker Games, Positional Games, Dominating Sets, Secure Domination, Heuristic Algorithms
Subject: Mathematics thesis
Thesis type: Masters
Completed: 2023
School: College of Science and Engineering
Supervisor: Michael Haythorpe