Hefetz, D., Krivelevich, M., Stojakovic, M., Szabó, T.
2014, X, 146 p. 13 illus., 8 illus. in color.
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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