Computing girth and cogirth in perturbed graphic matroids

TL;DR

This paper presents randomized polynomial-time algorithms for calculating girth and cogirth in binary matroids that are slight modifications of graphic matroids, advancing computational methods in matroid theory.

Contribution

It introduces the first efficient algorithms for girth and cogirth in low-rank perturbations of graphic matroids, a significant step in matroid algorithm research.

Findings

Algorithms run in polynomial time with randomized methods.

Effective for low-rank perturbations of graphic matroids.

Advances understanding of matroid girth and cogirth computation.

Abstract

We give polynomial-time randomized algorithms for computing the girth and the cogirth of binary matroids that are low-rank perturbations of graphic matroids.