Biased positional games and small hypergraphs with large covers

Michael Krivelevich*, Tibor Szabó

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We prove that in the biased (1:6) Hamiltonicity and k-connectivity Maker-Breaker games (k > 0 is a constant), played on the edges of the complete graph Kn, Maker has a winning strategy for 6 ≤ (log 2 - o(1))n/ log n. Also, in the biased (1 : 6) Avoider-Enforcer game played on E(Kn), Enforcer can force Avoider to create a Hamilton cycle when 6 ≤ (1 - o(1))n/ log n. These results are proved using a new approach, relying on the existence of hypergraphs with few edges and large covering number.

Original languageEnglish
Article numberR70
JournalElectronic Journal of Combinatorics
Volume15
Issue number1 R
DOIs
StatePublished - 5 May 2008

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