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- W4242064191 abstract "We study biased Maker/Breaker games on the edges of the complete graph, as introduced by Chvátal and Erdős. We show that Maker, occupying one edge in each of his turns, can build a spanning tree, even if Breaker occupies b ≤ (1 − o(1)) · edges in each turn. This improves a result of Beck, and is asymptotically best possible as witnessed by the Breaker-strategy of Chvátal and Erdős. We also give a strategy for Maker to occupy a graph with minimum degree c (where c = c(n) is a slowly growing function of n) while playing against a Breaker who takes b ≤ (1 − o(1)) · edges in each turn. This result improves earlier bounds by Krivelevich and Szabó. Both of our results support the surprising random graph intuition: the threshold bias is asymptotically the same for the game played by two “clever” players and the game played by two “random” players. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009" @default.
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- W4242064191 date "2009-12-01" @default.
- W4242064191 modified "2023-09-26" @default.
- W4242064191 title "Asymptotic random graph intuition for the biased connectivity game" @default.
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- W4242064191 doi "https://doi.org/10.1002/rsa.20279" @default.
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