A generalization of Fan's condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness

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 Benhocine and Wodja (1987).

[1]  John Adrian Bondy,et al.  Large cycles in graphs , 1971, Discret. Math..

[2]  John Adrian Bondy,et al.  A method in graph theory , 1976, Discret. Math..

[3]  A. Pawel Wojda,et al.  The Geng-Hua Fan conditions for pancyclic or Hamilton-connected graphs , 1987, J. Comb. Theory, Ser. B.

[4]  Geng-Hua Fan,et al.  New sufficient conditions for cycles in graphs , 1984, J. Comb. Theory, Ser. B.

[5]  S. Louis Hakimi,et al.  A cycle structure theorem for hamiltonian graphs , 1988, J. Comb. Theory, Ser. B.

[6]  O. Ore.  Note on Hamilton Circuits , 1960 .