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 Benhocine and Wodja (1987). © 1993.
Bedrossian, P., Chen, G., & Schelp, R. H. (1993). A generalization of Fan’s condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness. Discrete Mathematics, 115(1–3), 39–50. https://doi.org/10.1016/0012-365X(93)90476-A