This monograph is an outcome of the Oberwolfach Seminar on Positional Games, given by
the authors at the Mathematisches Forschungsinstitut Oberwolfach (MFO) in Oberwolfach …

Roughly speaking, the family of combinatorial games consists of two-player games with
perfect information (no hidden information as in some card games), no chance moves (no …

We study the algorithmic complexity of Maker–Breaker games played on the edge sets of
general graphs. We mainly consider the perfect matching game and the H-game. Maker …

In this paper we analyse classical Maker–Breaker games played on the edge set of a sparse
random board G~ n, p. We consider the Hamiltonicity game, the perfect matching game and …

For a positive integer k, we consider the k-vertex-connectivity game, played on the edge set
of K n, the complete graph on n vertices. We first study the Maker–Breaker version of this …

Positional games are a branch of combinatorics, researching a variety of two-player games,
ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract …

For a tree T on n vertices, we study the Maker-Breaker game, played on the edge set of the
complete graph on n vertices, which Maker wins as soon as the graph she builds contains a …

Given an increasing graph property F, the strong Avoider-Avoider F game is played on the
edge set of a complete graph. Two players, Red and Blue, take turns in claiming previously …

We study the biased (1: b) Maker–Breaker positional games, played on the edge set of the
complete graph on n vertices, Kn. Given Breaker's bias b, possibly depending on n, we …

Consider the following strong Ramsey game. Two players take turns in claiming a previously
unclaimed edge of the complete graph on n vertices until all edges have been claimed. The …