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On the (co)girth of a connected matroid
Journal article   Open access   Peer reviewed

On the (co)girth of a connected matroid

Jung Jin Cho, Yong Chen and Yu Ding
Discrete Applied Mathematics, Vol.155(18), pp.2456-2470
2007
DOI: 10.1016/j.dam.2007.06.015
url
https://doi.org/10.1016/j.dam.2007.06.015View
Published (Version of record) Open Access

Abstract

This article studies the girth and cogirth problems for a connected matroid. The problem of finding the cogirth of a graphic matroid has been intensively studied, but studies on the equivalent problem for a vector matroid or a general matroid have been rarely reported. Based on the duality and connectivity of a matroid, we prove properties associated with the girth and cogirth of a matroid whose contraction or restriction is disconnected. Then, we devise algorithms that find the cogirth of a matroid M from the matroids associated with the direct sum components of the restriction of M. As a result, the problem of finding the (co)girth of a matroid can be decomposed into a set of smaller sub-problems, which helps alleviate the computation. Finally, we implement and demonstrate the application of our algorithms to vector matroids.
Cogirth Girth Matroid connectivity Matroids

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