• DOI:10.1007/s00373-022-02588-7
• Corpus ID: 235446765

A generalization of a theorem of Nash-Williams

@article{Bauer2021AGO,
  title={A generalization of a theorem of Nash-Williams},
  author={Douglas Bauer and Linda M. Lesniak and Edward F. Schmeichel},
  journal={Graphs and Combinatorics},
  year={2021},
  volume={38}
}

• D. Bauer, L. Lesniak, E. Schmeichel
• Published 16 June 2021
• Materials Science
• 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 5$$\end{document}. In this note we generalize the Nash-Williams examples, and use this generalization to generate Ω2nn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega \left( \frac{2^n}{\sqrt{n}} \right) $$\end{document} forcibly hamiltonian n-sequences that do not satisfy Chvátal’s condition.