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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."
The theory of random graphs is a vital part of the education of any
researcher entering the fascinating world of combinatorics.
However, due to their diverse nature, the geometric and structural
aspects of the theory often remain an obscure part of the formative
study of young combinatorialists and probabilists. Moreover, the
theory itself, even in its most basic forms, is often considered
too advanced to be part of undergraduate curricula, and those who
are interested usually learn it mostly through self-study, covering
a lot of its fundamentals but little of the more recent
developments. This book provides a self-contained and concise
introduction to recent developments and techniques for classical
problems in the theory of random graphs. Moreover, it covers
geometric and topological aspects of the theory and introduces the
reader to the diversity and depth of the methods that have been
devised in this context.
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