The Ford-Fulkerson max ow labeling algorithm[3, 4] was introduced in the mid-1950's, and became the seminal work that is still applicable. The material presented in this note is taken from their book[5]. We are given a simple network with two speci ed nodes: source (s) and sink (t). Since the network is assumed to be simple, an arc is identi ed by its endpoints: (x; y) is the arc from node x to...

The tibial tubercle (interchangeable with tuberosity) is the most distal anchor of the extensor mechanism and can serve as a tool in altering patellofemoral (PF) mechanics. Known collectively as distal realignment procedures, osteotomies of the tibial tubercle are a useful method to treat a variety of PF conditions by allowing coronal, axial, and sagittal plane adjustments of the patellofemoral...

A Fano colouring is a colouring of the edges of a cubic graph by points of the Fano plane such that the colours of any three mutually adjacent edges form a line of the Fano plane. It has recently been shown by Holroyd and Škoviera (J. Combin. Theory Ser. B, to appear) that a cubic graph has a Fano colouring if and only if it is bridgeless. In this paper we prove that six, and conjecture that fo...

The present paper surveys important results in the theory of network flows which are not included in the book "Flows in Networks" by Ford and Fulkerson. The survey is divided into three areas: 1. Shortest paths and minimal cost flows, 2. Multi-terminal flows, 3. Multi-commodity flows.

A digraph whose degree sequence has a unique vertex labeled realization is called threshold. In this paper we present several characterizations of threshold digraphs and their degree sequences, and show these characterizations to be equivalent. Using this result, we obtain a new, short proof of the Fulkerson-Chen theorem on degree sequences of general digraphs.

A modification to the Dantzig and Fulkerson tanker scheduling problem is described. An insufficient number of vehicles and a utility associated with each vehicle delivery are assumed. The new problem is shown to be equivalent to a transshipment problem, the solution of which is the same as the maximal utility solution of the modified tanker scheduling problem. An example is given.

Computing a maximum weighted stable set in a bipartite graph is considered wellsolved and usually approached with preflow-push, Ford-Fulkerson or network simplex algorithms. We present a combinatorial algorithm for the problem that is not based on flows. Numerical tests suggest that this algorithm performs quite well in practice and is competitive with flow based algorithms especially in the ca...

We exhibit explicit constructions of contractors for the graph parameter counting the number of B-flows of a graph, where B is a subset of a finite Abelian group closed under inverses. These constructions are of great interest because of their relevance to the family of B-flow conjectures formulated by Tutte, Fulkerson, Jaeger, and others.