Fast Strategies In Maker–Breaker Games Played on Random Boards
Copyright policy )Fast Strategies In Maker–Breaker Games Played on Random Boards
In this paper we analyse classical Maker–Breaker games played on the edge set of a sparse random boardG~n,p. We consider the Hamiltonicity game, the perfect matching game and thek-connectivity game. We prove that forp(n) ≥ polylog(n)/nthe boardG~n,pis typically such that Maker can win these games asymptotically as fast as possible,i.e., withinn+o(n),n/2+o(n) andkn/2+o(n) moves respectively.
\(k\)-connectivity game, perfect matching game, Hamiltonicity game, Games on graphs (graph-theoretic aspects), Random graphs (graph-theoretic aspects), FOS: Mathematics, Mathematics - Combinatorics, Combinatorial games, Combinatorics (math.CO), Games involving graphs
\(k\)-connectivity game, perfect matching game, Hamiltonicity game, Games on graphs (graph-theoretic aspects), Random graphs (graph-theoretic aspects), FOS: Mathematics, Mathematics - Combinatorics, Combinatorial games, Combinatorics (math.CO), Games involving graphs
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).10 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!