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A sufficient condition for pancyclic graphs. (Chinese. English summary) Zbl 1110.05055

A graph \(G\) of order \(n\) is pancyclic if it contains a cycle of length \(k\) for each \(k=3,4,\dots, n\). This paper gives a sufficient condition for a graph to be pancyclic, that is, shows that for any integer \(t\geq 2\) and a \(2\)-connected graph with order \(n\) and minimum degree \(\delta\geq t\), if \(| N(u)\cup N(v)| \geq n-t\) for any two vertices with distance two in \(G\), then \(G\) is pancyclic unless either \(G\cong C_5\) or \(G\cong K_{n/2,n/2}\). This improves the result of J. Xu in [Acta Math. Appl. Sin. 24, No. 2, 310–313 (2001; Zbl 1003.05069)].

MSC:

05C38 Paths and cycles

Citations:

Zbl 1003.05069
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