Positional Games

Description

This text is based on a lecture course given by the authors in the framework of Oberwolfach Seminars at the Mathematisches Forschungsinstitut Oberwolfach in May, 2013. It is intended to serve as a thorough introduction to the rapidly developing field of positional games. This area constitutes an important branch of combinatorics, whose aim it is to systematically develop an extensive mathematical basis for a variety of two player perfect information games. These ranges from such popular games as Tic-Tac-Toe and Hex to purely abstract games played on graphs and hypergraphs. The subject of positional games is strongly related to several other branches of combinatorics such as Ramsey theory, extremal graph and set theory, and the probabilistic method. These notes cover a variety of topics in positional games, including both classical results and recent important developments. They are presented in an accessible way and are accompanied by exercises of varying difficulty, helping the reader to better understand the theory. The text will benefit both researchers and graduate students in combinatorics and adjacent fields Front Matter....Pages i-x Introduction....Pages 1-12 Maker-Breaker Games....Pages 13-25 Biased Games....Pages 27-42 Avoider-Enforcer Games....Pages 43-60 The Connectivity Game....Pages 61-74 The Hamiltonicity Game....Pages 75-83 Fast and Strong....Pages 85-96 Random Boards....Pages 97-112 The Neighborhood Conjecture....Pages 113-139 Back Matter....Pages 141-146