Abstract
Oxley has conjectured that for k≥4, if a matroid M has a k-element set that is the intersection of a circuit and a cocircuit, then M has a (k−2)-element set that is the intersection of a circuit and a cocircuit. In this paper we prove a stronger version of this conjecture for regular matroids. We also show that the stronger result does not hold for binary matroids.
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