On Packing T-Cuts

On the integral 4-packing of T-cuts

Let C = (V, E) be an undirected graph, w : E + Z’ a weight function and T c V an even subset of vertices from G. A T-cut is an edge-cut set which divides T into two odd sets. For ( Tj = 4 Seymour gave a good characterization of the graphs for which there exists a maximum packing of T-cuts that is integral. Based on Seymour’s characterization we provide a simple 0(n3m + PI”&) algorithm for incre...

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...

On a min-max theorem on bipartite graphs

Frank, Sebő and Tardos [4] proved that for any connected bipartite graft (G, T ), the minimum size of a T-join is equal to the maximum value of a partition of A, where A is one of the two colour classes of G. Their proof consists of constructing a partition of A of value |F |, by using a minimum T-join F. That proof depends heavily on the properties of distances in graphs with conservative weig...

Constructive procedures to solve 2-Dimensional Bin Packing Problems with Irregular Pieces and Guillotine Cuts

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cuttin...

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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