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New & Forthcoming Titles | Positional Games

Positional Games

Series: Oberwolfach Seminars, Vol. 44

Hefetz, D., Krivelevich, M., Stojakovic, M., Szabó, T.

2014, X, 146 p. 13 illus., 8 illus. in color.

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  • Unique, concise introductory text to the subject
  • Covers classical topics as well as recent very important developments
  • Relatively short, clear and self-contained text, accessible to a general mathematical audience only basic background in combinatorics is assumed
  • Theoretical material is accompanied by exercises of varying degree of difficulty

This text serves 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 range 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.

Content Level » Graduate

Keywords » Ramsey theory - positional games - random graphs

Related subjects » Applications

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.

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