An r-graph is an r-regular graph where every odd set of vertices is connected by at least r edges to the rest of the graph. Seymour conjectured that any r-graph is r + 1edge-colorable, and also that any r-graph contains 2r perfect matchings such that each edge belongs to two of them. We show that the minimum counter-example to either of these conjectures is a brick. Furthermore we disprove a va...

OBJECTIVES To assess the effectiveness of a modified tibial tubercle osteotomy as a treatment for arthroscopically diagnosed chondromalacia patellae. METHODS A total of 47 consecutive patients (51 knees) with arthroscopically proven chondromalacia, who had failed conservative management, underwent a modified Fulkerson tibial tubercle osteotomy. The mean age was 34.4 years (19.6 to 52.2). Pre-...

We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to directed graphs, while the second characterization says a digraph is split if and only if its degree sequence satisfies one of the Fulkerson inequalities (which de...

The max-flow and max-coflow problem on directed graphs is studied in the common generalization to regular spaces, i.e, to kernels or row spaces of totally unimodular matrices. Exhibiting a submodular structure of the family of paths within this model we generalize the Edmonds-Karp variant of the classical Ford-Fulkerson method and show that the number of augmentations is quadratically bounded i...

Matroids are discrete structures that capture independence under many different flavours. Our focus here is split between affine independence and transversal set theory. It was proved by Edmonds and Fulkerson in 1965 that the set of partial transversals of a set system are the independent sets of a matroid. A first attractive feature of these matroids (thus called transversal matroids) is that ...