✦ LIBER ✦
Cycle Bases for Lattices of Binary Matroids with No Fano Dual Minor and Their One-Element Extensions
✍ Scribed by Tamás Fleiner; Winfried Hochstättler; Monique Laurent; Martin Loebl
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 185 KB
- Volume
- 77
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we study the question of existence of a basis consisting only of cycles for the lattice Z(M) generated by the cycles of a binary matroid M. We show that if M has no Fano dual minor, then any set of fundamental circuits can be completed to a cycle basis of Z(M); moreover, for any one-element extension M$ of such a matroid M, any cycle basis for Z(M) can be completed to a cycle basis for Z(M$).