On the integral 4-packing of T-cuts

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We consider the maximum integral tWo-Commodity flow problem in augmented planar graphs (i.e., with both source-sink edges added) and provide an o(IVI 2 1ogIVI) algorithm for that problem. Let G = (V, E) be a graph and w : E-t Z+ a weight function. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. Lomonosov gave a good cha...

@bullet Technion -israel Institute of Technology Computer Science Department 2-trees Op-timal T-join and Integral Packing of T-cuts

Tight integral duality gap in the Chinese Postman problem

Let G = (V, E) be a graph and a weight function w : E -+ Z+. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. A T-join is a minimal subset of edges that meets every T-cut (a generalization of solutionS to the Chinese postman problem). The main theorem of this paper gives a tight upper bound on the difference between the ...

Connected Joins in Graphs

A join in a graph is a set F of edges such that for every circuit C, |C ∩ F | ≤ |C \ F |. We study the problem of finding a connected join covering a given subset of vertices of the graph, that is a Steiner tree which is a join at the same time. This turns out to contain the question of finding a T -join of minimum cardinality (or weight) which is, in addition, connected. This last problem is m...

A survey on T - joins , T - cuts , and conservative weightings , in : Combinatorics , Paul Erd

The book of L. Lovv asz and M. Plummer on matching theory includes a good overview of the topic indicated in the title. In the present paper we exhibit the main developments of the area in the last decade. After summarizing the basic concepts and their simple properties, we discuss several min-max theorems on packing T-cuts. Here the central result is a theorem of A. Seb} o on distances in a gr...