Vertices of Small Degree in Uniquely Hamiltonian Graphs
LetGbe a uniquely hamiltonian graph onnvertices. We show thatGhas a vertex of degree at mostclog28n+3, wherec=(2−log23)−1≈2.41. We show further thatGhas at least two vertices of degree less than four if it is planar and at least four vertices of degree two if it is bipartite.
Gespeichert in:
| Veröffentlicht in: | Journal of combinatorial theory. Series B 1998-11, Vol.74 (2), p.265-275 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | LetGbe a uniquely hamiltonian graph onnvertices. We show thatGhas a vertex of degree at mostclog28n+3, wherec=(2−log23)−1≈2.41. We show further thatGhas at least two vertices of degree less than four if it is planar and at least four vertices of degree two if it is bipartite. |
|---|---|
| ISSN: | 0095-8956 1096-0902 |
| DOI: | 10.1006/jctb.1998.1845 |