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

A celebrated result of Rödl and Ruciński states that for every graph-uniform hypergraphs for
which the threshold is determined by the asymmetric Ramsey problem in which a different …

In this paper we introduce a general framework for proving lower bounds for various
Ramsey type problems within random settings. The main idea is to view the problem from an …

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 …

Avoidance games are games in which two players claim vertices of a hypergraph and try to
avoid some structures. These games are studied since the introduction of the game of SIM in …

Waiter-Client games are played on some hypergraph $(X,\mathcal {F}) $, where $\mathcal
{F} $ denotes the family of winning sets. For some bias $ b $, during each round of such a …

Abstract We consider biased (1: b) Walker–Breaker games: Walker and Breaker alternately
claim edges of the complete graph K n, Walker taking one edge and Breaker claiming b …

Maker-Breaker games are played on a hypergraph (X,F), where F⊆2^X denotes the family
of winning sets. Both players alternately claim a predefined amount of edges (called bias) …

For a graph G, a monotone increasing graph property P and positive integer q, we define the
Client-Waiter game to be a two-player game which runs as follows. In each turn Waiter is …

We initiate the study of a new variant of the Maker-Breaker positional game, which we call
multistage game. Given a hypergraph H=(X, F) and a bias b≥ 1, the (1: b) multistage Maker …