✦ LIBER ✦
Regular matroids with every circuit basis fundamental
✍ Scribed by Wargo, Lawrence
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 434 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Hartvigsen and Zemel have obtained a characterization of those graphs which have every circuit basis fundamental. We consider the corresponding problem for binary matroids. We show that, in general, the class of binary matroids for which every circuit basis is fundamental is not closed under the taking of minors. However, this class is closed under the taking of series-minors. We also describe some general properties of this class of matroids. We end by extending Hartvigsen and Zemel's result to the class of regular matroids, thus obtaining a set of excluded minors which are graphic for this class.