A sharp threshold for the Hamilton cycle Maker-Breaker game
نویسندگان
چکیده
منابع مشابه
A sharp threshold for the Hamilton cycle Maker-Breaker game
We study the Hamilton cycle Maker-Breaker game, played on the edges of the random graph G(n, p). We prove a conjecture from [13], 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 Hamilto...
متن کاملA threshold for the Maker-Breaker clique game
We look at Maker-Breaker k-clique game played on the edge set of the random graph G(n, p). In this game, two players, Maker and Breaker, alternately claim unclaimed edges of G(n, p), until all the edges are claimed. Maker wins if he claims all the edges of a k-clique; Breaker wins otherwise. We determine that the property that Maker can win this game has a threshold at n− 2 k+1 , for all k > 3....
متن کاملOn the threshold for the Maker-Breaker H-game
We study the Maker-Breaker H-game played on the edge set of the random graph G(n, p). In this game, two players, Maker and Breaker, alternately claim unclaimed edges of G(n, p), until all the edges are claimed. Maker wins if he claims all the edges of a graph H; Breaker wins otherwise. Recently, Müller and Stojaković determined the threshold for the graph property that Maker can win this game i...
متن کاملDoubly Biased Maker-Breaker Connectivity Game
In this paper we study the (a : b) Maker-Breaker Connectivity game, played on the edge set of the complete graph on n vertices. We determine the winner for almost all values of a and b.
متن کاملRandom-Player Maker-Breaker games
In a (1 : b) Maker-Breaker game, one of the central questions is to find the maximal value of b that allows Maker to win the game (that is, the critical bias b∗). Erdős conjectured that the critical bias for many Maker-Breaker games played on the edge set of Kn is the same as if both players claim edges randomly. Indeed, in many Maker-Breaker games, “Erdős Paradigm” turned out to be true. There...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Structures and Algorithms
سال: 2009
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20252