A unified approach to box-Mengerian hypergraphs

A unified approach to box-Mengerian hypergraphs

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Article ID: iaor20106296
Volume: 35
Issue: 3
Start Page Number: 655
End Page Number: 668
Publication Date: Aug 2010
Journal: Mathematics of Operations Research
Authors: , ,
Abstract:

A hypergraph is called box-Mengerian if the linear system A x1, x0 is box-totally dual integral (box-TDI), where A is the edge-vertex incidence matrix of the hypergraph. Because it is NP-hard in general to recognize box-Mengerian hypergraphs, a basic theme in combinatorial optimization is to identify such objects associated with various problems. In this paper, we show that the so-called equitably subpartitionable (ESP) property, first introduced by Ding and Zang (2002) in their characterization of all graphs with the min-max relation on packing and covering cycles, turns out to be even sufficient for box-Mengerian hypergraphs. We also establish several new classes of box-Mengerian hypergraphs based on ESP property. This approach is of transparent combinatorial nature and is hence fairly easy to work with.

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