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Some excluded-minor theorems for a class of polymatroids

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Abstract

Problems involving representability are among the most frequently studied of all the problems in matroid theory. This paper considers the corresponding class of problems for polymatroids. A polymatroidh on the setS is representable over a free matroid or is Boolean if there is a map ϕ fromS into the set of subsets of a setV which preserves rank, that is for all subsetsA ofS,\(h(A) = \left| {\bigcup\limits_{a \in A} {\phi (a)} } \right|\). The class of Boolean polymatroids is minor-closed and in this paper we investigate the excluded minors of this class. In particular, we determine all such Boolean excluded minors that are 2-polymatroids.

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Author notes

  1. Geoff Whittle

    Present address: Mathematics Department, Victoria University of Wellington, Wellington, New England

Authors and Affiliations

  1. Mathematics Department, Louisiana State University, 70803, Baton Rouge, Louisiana, USA

    James Oxley

  2. Mathematics Department, University of Tasmania, 7001, Hobart, Tasmania, Australia

    Geoff Whittle

Authors
  1. James Oxley
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  2. Geoff Whittle
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Additional information

This research was partially supported by a grant from the Louisiana Education Quality Support Fund Through the Board of Regents

This research was supported by a grant from the Commonwealth of Australia through the Australian Research Council

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Oxley, J., Whittle, G. Some excluded-minor theorems for a class of polymatroids. Combinatorica 13, 467–476 (1993). https://doi.org/10.1007/BF01303518

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  • DOI: https://doi.org/10.1007/BF01303518

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