Game forms of Ramsey type problems.
Keywords: Ramsey, game, form, maker, breaker
TL;DR: In this paper we solve game forms of Ramsey type problems.
Abstract: Finding winning strategies in different games is important area of research. In this paper we focus on positional games only, i.e. games where players alternately color previously uncolored verticies and players goal is to color one of the winning sets. Despite simple definition it is showed that even this problem in PSPACE complete. It means that practical implementations of strategies are limited to heuristics and AI. However, purely mathematical strategies are still important, as they can be used to compare advanced methods to them (as a baseline) and because they require lesser amount computation. In this paper we discuss strategies for both Maker and Breaker which guarantee win under certain condition, meaning they can be used as starting points for programming strategies for concrete positional games that might include heuristics and AI.
From a mathematical point of view we study natural game version (maker-breaker game) of popular branch of combinatorics Ramsey type — Ramsey theory. Those games can be used to study Ramsey type problems, which is done in some recent articles. Here we talk about game forms of two families of problems (including open ones) and discuss how the strategies work in this case.
Submission Number: 37
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