A generalization of a theorem of Nash-Williams
Graphs and Combinatorics
Chvátal (J Combin Theory Ser B 12:163–168, 1972) 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 (Recent Trends in Graph Theory. Springer, Berlin, pp. 197–210, 1971) 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(2nn) forcibly hamiltonian n-sequences that do not satisfy Chvátal’s condition.
forcibly hamiltonian sequence, Hamiltonian graph, Nash-Williams sequence
Mathematics and Statistics
D. Bauer, L. Lesniak, and E. Schmeichel. "A generalization of a theorem of Nash-Williams" Graphs and Combinatorics (2022). https://doi.org/10.1007/s00373-022-02588-7