A generalization of Fan’s condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness. (English) Zbl 0773.05075

Authors’ abstract: A weakened version of Fan’s condition for Hamiltonicity is shown to be sufficient for a 2-connected graph to be pancyclic (with a few exceptions). Also, a similar condition is shown to be sufficient for a 3-connected graph to be Hamiltonian-connected. These results generalize the earlier work of A. Benhocine and A. P. Wojda [J. Comb. Theory, Ser. B 42, 167-180 (1987; Zbl 0613.05038)].


05C45 Eulerian and Hamiltonian graphs
05C40 Connectivity
05C38 Paths and cycles


Zbl 0613.05038
Full Text: DOI


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