Some excluded-minor theorems for a class of polymatroids |
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| Authors: | James Oxley Geoff Whittle |
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| Institution: | (1) Mathematics Department, Louisiana State University, 70803 Baton Rouge, Louisiana, USA;(2) Mathematics Department, University of Tasmania, 7001 Hobart, Tasmania, Australia;(3) Present address: Mathematics Department, Victoria University of Wellington, Wellington, New England |
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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  fromS into the set of subsets of a setV which preserves rank, that is for all subsetsA ofS,
. 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.This research was partially supported by a grant from the Louisiana Education Quality Support Fund Through the Board of RegentsThis research was supported by a grant from the Commonwealth of Australia through the Australian Research Council |
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| Keywords: | 05 B 35 |
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