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An elementary proof that every matroid is an intersection of principal transversal matroids

✍ Scribed by Geoffrey P. Whittle

Publisher: Elsevier Science
Year: 1985
Tongue: English
Weight: 60 KB
Volume: 54
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(85)90085-8

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✦ Synopsis

A principal transversal matroid is one containing a basis which spans all cyclic flats. A matroid M is the basis intersection of matroids M1,.. •, Mk if the bases of M are precisely the common bases of M1,..., Mk. Bondy and Welsh [2], Brualdi [3] and Bixby [1] have shown that every matroid is the basis intersection of principal transversal matroids. We strengthen the result using an elementary proof. We call a matroid near uniform if it contains at most one non spanning circuit.

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✍ Robert E. Bixby 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 192 KB

Wz give a new proof of a theorem of Bondy and Welsh. Our proof is simpler than previous ones in that it makes no use of Hall's theorem on tht: existence of a transversal of a family of sets.