On a generalization of Chvátal's condition giving new hamiltonian degree sequences

By imposing a structural criterion on a graph, we generalize the well-known Chvátal's sufficient condition for hamiltonicity (J. Combin. Theory Ser. B 12 (1972) 163-168). Using this result, we describe a new class of hamiltonian degree sequences which contains the sequences given by Chvátal's condition, as well as a class of degree sequences described by Fan and Liu (J. Systems Sci. Math. Sci. 4 (1) (1984) 27-32).