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Oriented Matroids and Hyperplane Transversals

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We prove that a finite family  of compact connected sets in R d has a hyperplane transversal if and only if for some k , 0< k < d , there exists an acyclic oriented matroid of rank k +1 on  such that every k +2 sets in  have an oriented k -transversal which meets the sets consistently with that oriented matroid.

Document Type: Research Article

Affiliations: 1: Indiana University,, Bloomington, Indiana, 4705-5701 2: Ohio State University, Columbus, Ohio, 43210

Publication date: April 1, 1996

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