For a finite graph G= (I’, E) Menger’s Theorem [6] states the following: if A, B c V then the minimal size of an A -B separating set of vertices (i.e., a set whose removal disconnects A from B), equals the maximal size of a set of disjoint A -B paths. This version of the theorem remains true, and quite easy to prove, also in the infinite case. To see this, take 9 to be a maximal (with respect t...

We introduce in this paper an exact nonlinear formulation of the multiway cut problem. By simple linearizations of this formulation, we derive several well-known and new formulations for the problem. We further establish a connection between the multiway cut and the maximum-weighted independent set problem. This leads to the study of several instances of the multiway cut problem through the the...

We consider the problem of finding an integral (and fractional) packing of branchings in a capacitated digraph with root-set demands. Schrijver described an algorithm that returns a packing with at most m + n3 + r branchings that makes at most m(m + n3 + r) calls to an oracle that basically computes a minimum cut, where n is the number of vertices, m is the number of arcs and r is the number of...

We present an extension to the subgradient algorithm to produce primal as well as dual solutions. It can be seen as a fast way to carry out an approximation of Dantzig-Wolfe decomposition. This gives a fast method for producing approximations for large scale linear programs. It is based on a new theorem in linear programming duality. We present successful experience with linear programs coming ...

In this paper we describe the problem of routing trains through a railway station. This routing problem is a subproblem of the automatic generation of timetables for the Dutch railway system. The problem of routing trains through a railway station is the problem of assigning each of the involved trains to a route through the railway station, given the detailed layout of the railway network with...

A simple graph is reflexive if its second largest eigenvalue λ2 is less than or equal to 2. A graph is a cactus, or a treelike graph, if any pair of its cycles (circuits) has at most one common vertex. For a lot of cactuses the property λ2 ≤ 2 can be tested by identifying and deleting a single cut-vetex (Theorem 1). if this theorem cannot be applied to a connected reflexive cactus and if all it...

Let C = (V, E) be an undirected graph, w : E + Z’ a weight function and T c V an even subset of vertices from G. A T-cut is an edge-cut set which divides T into two odd sets. For ( Tj = 4 Seymour gave a good characterization of the graphs for which there exists a maximum packing of T-cuts that is integral. Based on Seymour’s characterization we provide a simple 0(n3m + PI”&) algorithm for incre...

Copyright c © 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. edges among instances EX for each class (building connections between the entries within the same row, for every row of Z); last, we copy the edges among classes EC for each instance (building connections between the entries within the same column, for every column of Z). di 6= ∑m...

We show that every (sub)cubic n-vertex graph with sufficiently large girth has fractional chromatic number at most 2.2978 which implies that it contains an independent set of size at least 0.4352n. Our bound on the independence number is valid to random cubic graphs as well as it improves existing lower bounds on the maximum cut in cubic graphs with large girth.