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)
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.
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.
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)