English

Positional games on random graphs

Combinatorics 2007-05-23 v1 Probability

Abstract

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability pFp_{F} for the existence of Maker's strategy to claim a member of FF in the unbiased game played on the edges of random graph G(n,p)G(n,p), for various target families FF of winning sets. More generally, for each probability above this threshold we study the smallest bias bb such that Maker wins the (1b)(1\:b) biased game. We investigate these functions for a number of basic games, like the connectivity game, the perfect matching game, the clique game and the Hamiltonian cycle game.

Keywords

Cite

@article{arxiv.math/0601659,
  title  = {Positional games on random graphs},
  author = {Milos Stojakovic and Tibor Szabo},
  journal= {arXiv preprint arXiv:math/0601659},
  year   = {2007}
}