Let A be a binary matrix of size m × n, let cT be a positive row vector of length n and let e be the column vector, all of whose m components are ones.Expand

Proof. Let G satisfy the hypothesis of Theorem 1. Clearly, G contains a circuit ; let C be the longest one . If G has no Hamiltonian circuit, there is a vertex x with x ~ C . Since G is s-connected,… Expand

Two players play a game on the complete graph with n vertices. Each move of the first player consists of claiming k previously unclaimed edges, each move of the second player consists of claiming one… Expand

Consider a randomly generated boolean formula F (in the conjunctive normal form) with m clauses of size k over n variables; k is fixed at any value greater than 1, but n tends to infinity and m = (1 + o(1))cn for some c depending only on k.Expand

This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem, a problem that has inspired studies by mathematicians, chemists, and physicists.Expand

The toughness of a graph G is defined as the largest real number t such that deletion of any s points from G results in a graph which is either connected or else has at most s/t components.Expand