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.
On the quasi-transversals of a matroid
✍ Scribed by Richard A. Brualdi; Amélia Fonseca
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 220 KB
- Volume
- 146
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
We show that the set of r-quasi-transversals of a matroid, if nonempty, is the set of bases of a matroid. We also give an alternative proof of the known theorem which identifies the conjugate of the rank partition of a matroid.
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