Comparison of two techniques for proving nonexistence of strongly regular graphs (2009)
We show that the method of counting closed walks in strongly regular graphs rules out no parameter sets other than those ruled out by the method of counting eigenvalue multiplicities.
On Reichenbach's causal betweenness (2009)
Chvatal, Vasek, Wu, Baoyindureng
We characterize, by easily verifiable properties, abstract ternary relations isomorphic to the causal betweenness introduced by Hans Reichenbach.
On a Conjecture of Baïou and Balinski (2007)
We disprove a conjecture of Baou and Balinski concerning a variation on the Birkho-von Neumann theorem.
Campos, Victor, Chvatal, Vasek, Devroye, Luc, Taslakian, Perouz
A transversal in a rooted tree is any set of nodes that meets every path from the root to a leaf. We let c(T,k) denote the number of transversals of size k in a rooted tree T. We define a partial...
Sylvester-Gallai theorem and metric betweenness (2002)
Sylvester conjectured in 1893 and Gallai proved some forty years later that every finite set S of points in the plane includes two points such that the line passing through them includes either no...
TSP cuts which do not conform to the template paradigm (2001)
David Applegate, Robert Bixby, Vasek Chvatal, William Cook
The first computer implementation of the Dantzig-Fulkerson-Johnson cutting-plane method for solving the traveling salesman problem, written by Martin, used subtour inequalities as well as cutting...
Finding Cuts In The TSP (A preliminary report) (1995)
David Applegate, Robert Bixby, Vasek Chvatal, William Cook
TSPLIB is Gerhard Reinelt's library of some hundred instances of the traveling salesman problem. Some of these instances arise from drilling holes in printed circuit boards; others arise from...