A sufficient condition for pancyclism of Hamiltonian graphs. (Chinese) Zbl 1003.05069

Xu, Jun

Acta Math. Appl. Sin. 24, No. 2, 310-313 (2001).

The author proves the following result: Let \(G\) be a 2-connected graph with \(n\) vertices, \(\delta(G)\geq t\). If \(|N(u)\cup N(v)|\geq n-t\) for all nonadjacent vertices \(u\) and \(v\), then \(G\) is a pancyclic graph or \(n=2t\) and \(G= K_{t,t}\).

Reviewer: C.Lai (Zhangzhou)

MSC:

05C45	Eulerian and Hamiltonian graphs
05C38	Paths and cycles

Keywords:

2-connected graph; pancyclic graph