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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)].

MSC:
05C45 Eulerian and Hamiltonian graphs
05C40 Connectivity
05C38 Paths and cycles
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[1] Benhocine, A.; Wojda, A.P., The Geng-hua Fan conditions for pancyclic or Hamilton-connected graphs, J. combin. theory ser. B, 42, 167-180, (1987) · Zbl 0613.05038
[2] Bondy, J.A., Large cycles in graphs, Discrete math., 1, 121-132, (1971) · Zbl 0224.05120
[3] Bondy, J.A.; Chvat́al, V., A method in graph theory, Discrete math., 15, 111-136, (1976) · Zbl 0331.05138
[4] Fan, Geng-Hua, New sufficient conditions for cycles in graphs, J. combin. theory ser. B, 37, 221-227, (1984) · Zbl 0551.05048
[5] Ore, O., Note on Hamilton circuits, Amer. math. monthly, 67, 55, (1960) · Zbl 0089.39505
[6] Schmeichel, E.F.; Hakimi, S.L., A cycle structure theorem for Hamiltonian graphs, J. combin. theory ser. B, 45, 99-107, (1988) · Zbl 0607.05050
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