The unbreakable quasi-graphic matroids
Combinatorics
2026-05-14 v1
Abstract
A matroid M is unbreakable if it is connected and M/F is connected for every flat F of M . Oxley and Pfeil characterized the unbreakable graphic matroids, and Fife, Mayhew, Oxley, and Semple characterized the graphs underlying 3-connected unbreakable frame matroids. We extend the latter result by giving a complete characterization of the 3-connected unbreakable quasi-graphic matroids. As a special case we obtain a characterization of the 3-connected lifted-graphic matroids.
Keywords
Cite
@article{arxiv.2605.12811,
title = {The unbreakable quasi-graphic matroids},
author = {Sayantani Bhattacharya and John David Clifton and Zach Walsh},
journal= {arXiv preprint arXiv:2605.12811},
year = {2026}
}