Spanning cycles in regular matroids without small cocircuits

AbstractA 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)>n5−1, 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)−45,6}, then M has a spanning cycle