Spanning cycles in regular matroids without small cocircuits

作者：Li Ping^*; Lai Hong Jian; Shao Yehong; Zhan Mingquan

来源：European Journal of Combinatorics, 2012, 33(8): 1765-1776.

DOI：10.1016/j.ejc.2012.03.033

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 %26gt; 16 vertices, and if delta(G) %26gt; 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, vertical bar D vertical bar %26gt;= max {r(M)-4/5, 6}, then M has a spanning cycle.

• 出版日期2012-11
• 单位新疆大学; 北京交通大学