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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

Citations:

Zbl 0613.05038
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References:

[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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