Positional games on random graphs

Authors:
Miloš Stojaković;Tibor Szabó
Affiliations:
Institute of Theoretical Computer Science, ETH Zurich, CH-8092 Switzerland;Institute of Theoretical Computer Science, ETH Zurich, CH-8092 Switzerland
Venue:
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Year:
2005

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Abstract

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability pℱ for the existence of Maker's strategy to claim a member of ℱ in the unbiased game played on the edges of random graph G(n, p), for various target families ℱ of winning sets. More generally, for each probability above this threshold we study the smallest bias b such that Maker wins the (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. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005