Cycle bases for lattices of matroids with no Fano dual minor and their one-element extensions

Fleiner, Tamas and Hochstättler, Winfried and Laurent, Monique and Loebl, Martin (1999) Cycle bases for lattices of matroids with no Fano dual minor and their one-element extensions.
Published in: Journal of Combinatorial Theory : Series B Vol. 77 (1). pp. 25-38.

Abstract

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 matroid M, any cycle basis for Z(M) can be completed to a cycle basis for Z(M). This is a revised version of 96-249. The major change is a considerable simplification of the proof of Theorem 3.1 contributed by Tamas Fleiner which gives additional insight into the structure.


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Deposit Information:
ZAIK Number: zpr98-337
Depositing User: Winfried Hochstättler
Date Deposited: 02 Apr 2001 00:00
Last Modified: 16 Jan 2012 14:28
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/337