Spanning cycles in regular matroids without small cocircuits

Authors:
Ping Li;Hong-Jian Lai;Yehong Shao;Mingquan Zhan
Affiliations:
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China and Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA;College of Arts and Sciences, Ohio University Southern, OH 45638, USA;Department of Mathematics, Millersville University, Millersville, PA 17551, USA
Venue:
European Journal of Combinatorics
Year:
2012

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Abstract

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 n16 vertices, and if @d(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.