Determining a binary matroid from its small circuits
It is well known that a rank-r matroid M is uniquely determined by its circuits of size at most r. This paper proves that if M is binary and r ≥ 3, then M is uniquely determined by its circuits of size at most r - 1 unless M is a binary spike or a special restriction thereof. In the exceptional cases, M is determined up to isomorphism.
Publication Source (Journal or Book title)
Electronic Journal of Combinatorics
Oxley, J., Semple, C., & Whittle, G. (2016). Determining a binary matroid from its small circuits. Electronic Journal of Combinatorics, 23 (1) https://doi.org/10.37236/5373