Some excluded-minor theorems for a class of polymatroids

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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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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AMS subject classification code (1991)

  • 05 B 35