Spanning cycles in regular matroids without small cocircuits

A cycle of a matroid is a disjoint union of circuits. A cycle C of a matroid M is spanning if the rank of C equals the rank of M . Settling an open problem of Bauer in 1985, Catlin in [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44] showed that if G is a 2-connected graph on n > 16 vertices, and if δ ( G ) > n 5 − 1 , then G has a spanning cycle. Catlin also showed that the lower bound of the minimum degree in this result is best possible. In this paper, we prove that for a connected simple regular matroid M , if for any cocircuit D , | D | ≥ max { r ( M ) − 4 5 , 6 } , then M has a spanning cycle.