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Restricted b-factors in bipartite graphs and t-designs

✍ Scribed by Ivette Arámbula; Illya V. Hicks

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
178 KB
Volume
14
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

We present a new equivalence result between restricted b‐factors in bipartite graphs and combinatorial t‐designs. This result is useful in the construction of t‐designs by polyhedral methods. We propose a novel linear integer programming formulation, which we call GDP, for the problem of finding t‐designs that has a noteworthy advantage compared to the traditional set‐covering formulation. We analyze some polyhedral properties of GPD, implement a branch‐and‐cut algorithm using it and solve several instances of small designs to compare with another point‐block formulation found in the literature. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 169–182, 2006

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