A branch-and-cut algorithm for the capacitated profitable tour problem.

We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and well-known integer polytopes — the cut, boolean quadric, multicut and clique partitioning polytopes — are shown to arise as projections of binary psd polyt...

The motivation for Core Logic is explained. Its system of proof is set out. It is then shown that, although the system has no Cut rule, its relation of deducibility obeys Cut with epistemic gain. §1. The debate over logical reform. There is much dispute over which logic is the right logic—indeed, over whether there could even be such a thing as the right logic, rather than a spectrum of logics ...

In 1972, M. Rosenfeld asked if every triangle-free graph could be embedded in the unit sphere S in such a way that two vertices joined by an edge have distance more than √ 3 (i.e. distance more than 2π/3 on the sphere). In 1978, D. Larman [4] disproved this conjecture, constructing a triangle-free graph for which the minimum length of an edge could not exceed p 8/3. In addition, he conjectured ...

This note investigates the boundary between polynomially-solvable Max Cut and NP Hard Max Cut instances when they are classified only on the basis of the sign pattern of the objective function coefficients, i.e., of the orthant containing the objective function vector. It turns out that the matching number of the subgraph induced by the positive edges is the key parameter that allows us to diff...

x To acknowledge the corn-This purely American expression means to admit the losing of an argument , especially in regard to a detail; to retract; to admit defeat. It is over a hundred years old. Andrew Stewart, a member of Congress, is said to have mentioned it in a speech in 1828. He said that haystacks and cornfields were sent by Indiana, Ohio and Kentucky to Philadelphia and New York. Charl...

The max-cut problem asks for partitioning the nodes V of a graph G = (V,E) into two sets (one of which might be empty), such that the sum of weights of edges joining nodes in different partitions is maximum. Whereas for general instances the max-cut problem is NPhard, it is polynomially solvable for certain classes of graphs. For planar graphs, there exist several polynomial-time methods determ...