Recently Hochstättler and Nešetřil introduced the flow lattice of an oriented matroid as generalization of the lattice of all integer flows of a digraph or more general a regular matroid. This lattice is defined as the integer hull of the characteristic vectors of signed circuits. Here, we characterize the flow lattice of oriented matroids that are uniform… (More)
1 Motivation Signed graphs have been studied a lot during the last two decades. We address the vertex disjoint negative cycle packing problem posed by Zaslavsky [7, Problem II.A.1a]. Our aim is to find two vertex disjoint negative cycles in reasonable time which generalizes the problem of finding two vertex disjoint odd cycles in a graph. In the first stage… (More)
We describe a new solution approach for order sequencing which reflects the build-to-order strategy of the European automobile industry. Therefore, it has to cope with a daily changing variety of customer orders. Each order consists of a set of commodities which are implemented while the order sequence passes through a body shop, a paint shop, and an… (More)
We prove that the chromatic number of an oriented matroid O of rank r ≥ 3 is at most r +1 with equality if and only if O is the oriented matroid of an orientation of Kr+1, the complete graph on r + 1 vertices.
We derive a polynomial time algorithm to compute a stable solution in a mixed matching market from an auction procedure as presented by Eriksson and Karlander . As a special case we derive an O(nm) algorithm for bipartite matching that does not seem to have appeared in the literature yet.