The unbreakable frame matroids
A connected matroid M is unbreakable if, for each of its flats F, the matroid M/F is connected or, equivalently, if M*has no two skew circuits. Pfeil showed that a simple graphic matroid M(G) is unbreakable exactly when M(G) is either a cycle or a complete graph. We extend this result to describe which graphs are the underlying graphs of unbreakable frame matroids.
Publication Source (Journal or Book title)
SIAM Journal on Discrete Mathematics
Fife, T., Mayhew, D., Oxley, J., & Semple, C. (2020). The unbreakable frame matroids. SIAM Journal on Discrete Mathematics, 34 (3), 1522-1537. https://doi.org/10.1137/19M126428X