Name
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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.ejc.2012.03.033 | Eur. J. Comb. |
Keywords | Field | DocType |
disjoint union,small cocircuits,connected simple regular matroid,matroid m,minimum degree,j. graph theory,spanning cycle,n16 vertex,2-connected graph,cycle c,cocircuit d,eulerian subgraphs,regular matroids | Matroid,Discrete mathematics,Combinatorics,Cycle basis,Matroid partitioning,Graphic matroid,Regular matroid,Spanning tree,Circuit rank,Weighted matroid,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 8 | 0195-6698 |
Citations | PageRank | References |
1 | 0.35 | 10 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ping Li | 1 | 21 | 7.14 |
| Hong-Jian Lai | 2 | 631 | 97.39 |
| Yehong Shao | 3 | 102 | 14.70 |
| Mingquan Zhan | 4 | 86 | 12.03 |