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). © 2004 Elsevier B.V. All rights reserved.
Stacho, L., & Szeszlér, D. (2005). On a generalization of Chvátal’s condition giving new hamiltonian degree sequences. Discrete Mathematics, 292(1–3), 159–165. https://doi.org/10.1016/j.disc.2004.12.002