Name
Abstract | ||
|---|---|---|
A graph G on n vertices is called subpancyclic if it contains cycles of every length k with 3 ⩽ k ⩽ c ( G ), where c ( G ) denotes the length of a longest cycle in G ; if moreover c ( G ) = n , then G is called pancyclic . By a result of Flandrin et al. a claw-free graph (on at least 35 vertices) with minimum degree at least 1 3 (n − 2) is pancyclic. This degree bound is best possible. We prove that for a claw-free graph to be subpancyclic we only need the degree condition δ > √3 n + 1 − 2. Again, this degree bound is best possible. It follows directly that under the same condition a hamiltonian claw-free graph is pancyclic. |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1016/S0012-365X(98)00278-7 | Discrete Mathematics |
Keywords | Field | DocType |
(sub)pancyclic,(hamilton) cycle,circumference,05c35,claw-free hamiltonian graph,05c38,claw-free graph,05c45,hamiltonian graph,claw free graph,hamilton cycle | Discrete mathematics,Graph toughness,Combinatorics,Bound graph,Graph power,Quartic graph,Cycle graph,Regular graph,Degree (graph theory),Mathematics,Pancyclic graph | Journal |
Volume | Issue | ISSN |
197-198, | 1-3 | Discrete Mathematics |
Citations | PageRank | References |
4 | 0.71 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. Trommel | 1 | 11 | 1.77 |
| H. J. Veldman | 2 | 262 | 44.44 |
| A. Verschut | 3 | 4 | 0.71 |