Let G be a 2-connected plane graph with outer cycle XG such that for every minimal vertex cut S of G with IS1 5 3, every component of G \ S contains a vertex of XG. A sufficient condition for G to be Hamiltonian is presented. This theorem generalizes both Tutte's theorem that every 4-connected plan
Hamilton Cycles in Planar Graphs and Venn Diagrams
β Scribed by Kiran B. Chilakamarri; Peter Hamburger; Raymond E. Pippert
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 258 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
Using graph theory, we prove Gru nbaum's conjecture: Every Venn diagram of n curves can be extended to a Venn diagram of n+1 curves by the addition of a suitable simple closed curve.
π SIMILAR VOLUMES
## UNIVERSIW OF WATERLOO ' The research reported here has been sponsored by the Canadian Commonwealth Association.
## Abstract We prove that the strong product of any __n__ connected graphs of maximum degree at most __n__ contains a Hamilton cycle. In particular, __G__^Ξ(__G__)^ is hamiltonian for each connected graph __G__, which answers in affirmative a conjecture of Bermond, Germa, and Heydemann. Β© 2005 Wile