Positional Games by Dan HefetzPositional Games by Dan Hefetz

Positional Games

byDan Hefetz, Michael Krivelevich, Milo Stojakovi

Paperback | July 3, 2014

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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.
Dan Hefetz obtained his PhD in computer science at Tel Aviv University and is lecturer in pure mathematics at the University of Birmingham. Michael Krivelevich obtained his PhD in mathematics at Tel Aviv University, Israel, where he is now a full professor. MiloÅ¡ StojakoviÄ obtained his PhD in computer science at ETH Zürich, Switzerla...
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Title:Positional GamesFormat:PaperbackDimensions:146 pagesPublished:July 3, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034808240

ISBN - 13:9783034808248

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Table of Contents

Preface.- 1 Introduction.- 2 Maker-Breaker Games.- 3 Biased Games.- 4 Avoider-Enforcer Games.- 5 The Connectivity Game.- 6 The Hamiltonicity Game.- 7 Fast and Strong.- 8 Random Boards.- 9 The Neighborhood Conjecture.- Bibliography.