منابع مشابه
Positional games on random graphs
We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability pF for the existence of Maker’s strategy to claim a member of F in the unbiased game played on the edges of random graph G(n, p), for various target families F of winning sets. More generally, for each probability above this threshold we study the smallest bias...
متن کاملOn unbiased games on random graphs
We study unbiased Maker-Breaker positional games played on the edges of the random graph G(n, p). As the main result of the paper, we prove a conjecture from [18], that the property that Maker is able to win the Hamiltonicity game played on a random graph G(n, p) has a sharp threshold at log n n . Our theorem can be considered a game-theoretic strengthening of classical results from the theory ...
متن کاملOn Balanced Coloring Games in Random Graphs
Consider the balanced Ramsey game, in which a player has r colors and where in each round r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color to each edge and her goal is to avoid creating a monochromatic copy of some fixed graph F for as long as possible. The Achlioptas game is similar, but the player only loses when sh...
متن کاملStrong Games Played on Random Graphs
Did you ever play games such as Tic-Tac-Toe, its close relative n-in-a-row or Hex? Then you are already familiar with strong games. Strong games, as a specific type of Positional games, involve two players alternately claiming unoccupied elements of a set X, which is referred to as the board of the game. The two players are called Red (the first player) and Blue (the second player). The focus o...
متن کاملBalanced Avoidance Games on Random Graphs
We introduce and study balanced online graph avoidance games on the random graph process. The game is played by a player we call Painter. Edges of the complete graph with n vertices are revealed two at a time in a random order. In each move, Painter immediately and irrevocably decides on a balanced coloring of the new edge pair: either the first edge is colored red and the second one blue or vi...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2005
ISSN: 1042-9832
DOI: 10.1002/rsa.20059