TY - JOUR
T1 - A sharp threshold for the hamilton cycle Maker-Breaker game
AU - Hefetz, Dan
AU - Krivelevich, Michael
AU - Stojakovič, Miloš
AU - Szabó, Tibor
PY - 2009/1
Y1 - 2009/1
N2 - We study the Hamilton cycle Maker-Breaker game, played on the edges of the random graph G(n,p). We prove a conjecture from (Stojaković and Szabó, Random Struct and Algorithms 26 (2005), 204-223.), asserting that the property that Maker is able to win this game, has a sharp threshold at log n/n. Our theorem can be considered a game-theoretic strengthening of classical results from the theory of random graphs: not only does G(n,p) almost surely admit a Hamilton cycle for p = (1 + ε) log n/n, but Maker is able to build one while playing against an adversary.
AB - We study the Hamilton cycle Maker-Breaker game, played on the edges of the random graph G(n,p). We prove a conjecture from (Stojaković and Szabó, Random Struct and Algorithms 26 (2005), 204-223.), asserting that the property that Maker is able to win this game, has a sharp threshold at log n/n. Our theorem can be considered a game-theoretic strengthening of classical results from the theory of random graphs: not only does G(n,p) almost surely admit a Hamilton cycle for p = (1 + ε) log n/n, but Maker is able to build one while playing against an adversary.
KW - Combinatorial games
KW - Hamilton cycle
KW - Random graph
UR - http://www.scopus.com/inward/record.url?scp=60349097895&partnerID=8YFLogxK
U2 - 10.1002/rsa.20252
DO - 10.1002/rsa.20252
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AN - SCOPUS:60349097895
SN - 1042-9832
VL - 34
SP - 112
EP - 122
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
IS - 1
ER -