The Picker-Chooser diameter game
نویسنده
چکیده
Positional Games are played under several rules on the same hypergraph. We consider some intriguing connection among the outcome of the Maker-Breaker and the Picker-Chooser versions. The later ones were introduced by Beck in [5] and proved to be important in understanding Positional Games in general. Beck had the profound conjecture that playing on the same hypergraph, Picker has better chances than Maker. Our main goal is to confirm this conjecture for the notoriously hard diameter-2 game, that was studied by Balogh et al. in [1]. The diameter-2 game is also an example that the probabilistic intuition, or “Erdős paradigm” can fail completely, but the acceleration of the game can restore it. The Picker-Chooser version are closer to Erdős paradigm, there are almost matching lower and upper bounds for the critical density. Pursuing these goals, we extend the theory of Picker-Chooser games to biased and discrepancy games, and develop Erdős-Selfridge type of results.
منابع مشابه
On the Complexity of Chooser-picker Positional Games
Two new versions of the so-called Maker-Breaker Positional Games are defined by József Beck in [Combinatorica 22(2) (2002) 169–216]. He defines two players, Picker and Chooser. In each round, Picker takes a pair of elements not already selected and Chooser keeps one and returns the other to Picker. In the Picker-Chooser version Picker plays as Maker and Chooser plays as Breaker, while the roles...
متن کاملOn Chooser-Picker positional games
Two new versions of the so-called Maker-Breaker Positional Games are defined by József Beck. In these variants Picker takes unselected pair of elements and Chooser keeps one of these elements and gives back the other to Picker. In the Picker-Chooser version Picker is Maker and Chooser is Breaker, while the roles are swapped in the Chooser-Picker version. It seems that both the Picker-Chooser an...
متن کاملManipulative Waiters with Probabilistic Intuition
For positive integers n and q and a monotone graph property A, we consider the two player, perfect information game WC(n, q,A), which is defined as follows. The game proceeds in rounds. In each round, the first player, called Waiter, offers the second player, called Client, q + 1 edges of the complete graph Kn which have not been offered previously. Client then chooses one of these edges which ...
متن کاملA Path Guessing Game with Wagering
We consider a two-player game in which the first player (the Guesser) tries to guess, edgeby-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of her guess, and receives a payoff proportional to her wager if she is correct. We derive optimal strategies for both players for various classes of graphs, and ...
متن کاملProximal and Semi-proximal Spaces
Proximal and semi-proximal spaces are defined with the help of a game played on uniform spaces. Proximal spaces are where the entourage-picker has a winning strategy, and semi-proximal spaces are where the opponent, the point-picker, does not have a winning strategy. The class of proximal spaces is closed under Σ-products and closed subspaces. In this paper it is shown that product of two semi-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 411 شماره
صفحات -
تاریخ انتشار 2010