In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A, B of its vertex set, such that every transitive subset of A is in the out-neighbour set of some vertex in B, and vice… (More)
An important instance of the Caccetta-Häggkvist conjecture asserts that an n-vertex digraph with minimum outdegree at least n/3 contains a directed triangle. Improving on a previous bound of 0.3532n due to Hamburger, Haxell, and Kostochka we prove that a digraph with minimum outdegree at least 0.3465n contains a directed triangle. The proof is an… (More)
In an-approximate Nash equilibrium, a player can gain at most in expectation by unilateral deviation. An-well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with positive probability must have payoff within of the best response payoff. Daskalakis, Mehta and Papadimitriou  conjectured that every win-lose… (More)
We prove that if every subgraph of a graph G has a balanced separation of order at most a then G has treewidth at most 105a. This establishes a linear dependence between the treewidth and the separation number.
We examine strategy-proof elections to select a winner amongst a set of agents, each of whom cares only about winning. This impartial selection problem was introduced independently by Holzman and Moulin  and Alon et al. . Fisher and Klimm  showed that the permutation mechanism is impartial and 1 2-optimal, that is, it selects an agent who gains, in… (More)
We prove that for any constant k and any < 1, there exist bimatrix win-lose games for which every-WSNE requires supports of cardinality greater than k. To do this, we provide a graph-theoretic characterization of win-lose games that possess-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight  to construct… (More)
*Please remember to scan your meal card at the host/hostess station in the dining room for each meal. MEETING ROOMS All lectures will be held in Max Bell 159 (Max Bell Building accessible by walkway on 2nd floor of Corbett Hall). LCD projector, overhead projectors and blackboards are available for presentations. Note that the meeting space designated for… (More)