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

THE CRITICAL BIAS FOR THE HAMILTONICITY GAME IS (1 + o(1))n/ ln n 1. Introduction A
Maker-Breaker game is a triple (H, a, b), wh Page 1 JOURNAL OF THE AMERICAN …

We prove that in the biased $(1: b) $ Hamiltonicity and $ k $-connectivity Maker-Breaker
games ($ k> 0$ is a constant), played on the edges of the complete graph $ K_n $, Maker …

Abstract The Maker–Breaker domination game is played on a graph G by two players, called
Dominator and Staller, who alternately choose a vertex that has not been played so far …

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 …

An Avoider–Enforcer game is played by two players, called Avoider and Enforcer, on a
hypergraph F⊆ 2X. The players claim previously unoccupied elements of the board X in …

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 study NP-hard Chooser–Picker biased games on hypergraphs and their connections to
classic Maker–Breaker games. We prove two weight-function-based winning criteria for …

ABSTRACT We study the Maker‐Breaker k‐clique game played on the edge set of the
random graph G (n, p). In this game, two players, Maker and Breaker, alternately claim …

Given a graph $ G $ and positive integers $ n $ and $ q $, let ${\bf G}(G; n, q) $ be the game
played on the edges of the complete graph $ K_n $ in which the two players, Maker and …