Name
Abstract | ||
|---|---|---|
An edge e of a minimally 3-connected graph G is non-essential if and only if the graph obtained by contracting e from G is both 3-connected and simple. Suppose that G is not a wheel. Tutte's Wheels Theorem states that G has at least one non-essential edge. We show that each longest cycle of G contains at least two non-essential edges. Moreover, each cycle of G whose edge set is not contained in a fan contains at least two non-essential edges. We characterize the minimally 3-connected graphs which contain a longest cycle containing exactly two non-essential edges. |
Year | DOI | Venue |
|---|---|---|
1997 | 10.1006/jctb.1997.1720 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
wheels theorem,longest cycle version,connected graph | Tutte 12-cage,Discrete mathematics,Combinatorics,Tutte theorem,Polyhedral graph,Cycle graph,Graph minor,Multiple edges,Mathematics,Graph coloring,Tutte matrix | Journal |
Volume | Issue | ISSN |
70 | 1 | Journal of Combinatorial Theory, Series B |
Citations | PageRank | References |
3 | 0.78 | 13 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Talmage James Reid | 1 | 48 | 12.18 |
| Haidong Wu | 2 | 26 | 8.43 |