A generalization of a theorem of Nash-Williams

Abstract

In [4], Chvátal gave a well-known sufficient condition for a graphical sequence to be forcibly hamiltonian, and showed that in some sense his condition is best possible. Nash-Williams [7] gave examples of forcibly hamiltonian n−sequences that do not satisfy Chvátal's condition, for every n ≥ 5. In this note we generalize the Nash-Williams examples, and use this generalization to generate Ω( 2 n √ n ) forcibly hamiltonian n−sequences that do not satisfy Chvátal's condition.