A result of Plotkin, Rao, and Smith implies that graphs with polynomial expansion have strongly sublinear separators. We prove a converse of this result showing that hereditary classes of graphs withâ€¦ (More)

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 thatâ€¦ (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 theâ€¦ (More)

Let ES(n) be the minimal integer such that any set of ES(n) points in the plane in general position contains n points in convex position. The problem of estimating ES(n) was first formulated by ErdÅ‘sâ€¦ (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 graphtheoreticâ€¦ (More)

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 andâ€¦ (More)

We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced)â€¦ (More)