The Circuit-Cocircuit Intersection Conjecture for Intersection Size $k\le 6$

Abstract

Oxley conjectured (1992) that if a matroid has a circuit-cocircuit intersection of size $k\ge 4$, it has a circuit-cocircuit intersection of size $k-2$. We show that this conjecture holds for $k\le 6$.

arXiv comment5 pages