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...

In this paper we consider the class of simple graphs defined by excluding, as inducedsubgraphs, even holes (i.e. chordless cycles of even length). These graphs are known aseven-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, thatuses star cutsets and 2-joins. This is a significant strengthening of the only other pre-viously known decomposition of ev...

We consider a family of sequent systems with “well-behaved” logical rules in which the cut rule and/or the identity-axiom are not present. We provide a semantic characterization of the logics induced by these systems in the form of non-deterministic three-valued or four-valued matrices. The semantics is used to study some important proof-theoretic properties of these systems. These results shed...

For conflict resolution between local coordination modules of distributed agents, synthesized based on inter-agent constraints, two original ideas are proposed. The first is a designer-comprehensible Distributed Constraint Specification Network (DCSN) for describing the constraint relationships among agents. The second is an algorithm using cutset theory for generating, from a given DCSN, an AN...

We calculate Yukawa interactions at one-loop on intersecting D6 branes. We demonstrate the non-renormalization theorem in supersymmetric configurations, and show how Yukawa β-functions may be extracted. In addition to the usual logarithmic running, we find the power-law dependence on the infra-red cut-off associated with Kaluza-Klein modes. Our results may also be used to evaluate coupling reno...