An isoperimetric minimax

An Asymptotic Isoperimetric Inequality

For a finite metric space V with a metric ρ, let V n be the metric space in which the distance between (a1, . . . , an) and (b1, . . . , bn) is the sum ∑n i=1 ρ(ai, bi). We obtain an asymptotic formula for the logarithm of the maximum possible number of points in V n of distance at least d from a set of half the points of V , when n tends to infinity and d satisfies d √ n. 1 The Main Results Le...

An isoperimetric le

Bialostocki, A. and P. Dierker, An isoperimetric lemma, Discrete Mathematics 94 (1991) 221-228. A continuous version of the following problem is solved: Let G be a multipartite graph with a given partition of its vertex set, A, U A, U U A,,,. Find the maximum possible number of edges in G such that G has no connected component with more then t vertices.

An isoperimetric comparison theorem

An Ordinal Minimax Theorem

One of the earliest solution concepts considered in game theory are saddle points, combinations of actions such that no player can gain by deviating (see, e.g., von Neumann and Morgenstern, 1947). In two-player zero-sum games, every saddle point happens to coincide with the optimal outcome both players can guarantee in the worst case and thus enjoys a very strong normative foundation. Unfortuna...

An Isoperimetric Function for Stallings’ Group

We prove that n is an isoperimetric function for a group of Stallings that is finitely presented but not of type F3.