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

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 …

In this paper we analyze biased Maker‐Breaker games and Avoider‐Enforcer games, both
played on the edge set of a random board. In Maker‐Breaker games there are two players …

We present a general approach connecting biased Maker‐Breaker games and problems
about local resilience in random graphs. We utilize this approach to prove new results and …

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 …

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 …

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 …

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 …

In this dissertation we present current developments on Hamilton cycles and spanning trees
in random graphs as well as in (very) dense hypergraphs. These results include an …