We prove that if a graph G on n > 32 vertices is hamiltonian and has two nonadjacent vertices u and u with d(u) + d(u) 3 n + z where z = 0 if n is odd and z = 1 if n is even, then G contains all cycles of length m where 3 < m < 1/5(n + 13).
Polyhedral graphs without hamiltonian cycles
β Scribed by Hansjoachim Walther
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 309 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0166-218X
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β¦ Synopsis
There is a constructed sequence of polyhedral cyclically 5-connected cubic non-hamiltonian graphs having only 5-gons and 8-gons as faces.
π SIMILAR VOLUMES
We investigate the values of t(n), the maximum number of edges in a graph with n vertices and not containing a four-cycle. Techniques for finding these are developed and the values of t(n) for all n up to 21 are obtained. All the corresponding extremal graphs are found.
## Abstract A graph __G__ of order at least 2__n__+2 is said to be __n__βextendable if __G__ has a perfect matching and every set of __n__ independent edges extends to a perfect matching in __G__. We prove that every pair of nonadjacent vertices __x__ and __y__ in a connected __n__βextendable graph
## Abstract A group Ξ is said to possess a hamiltonian generating set if there exists a minimal generating set Ξ for Ξ such that the Cayley color graph __D__~Ξ~(Ξ) is hamiltonian. It is shown that every finite abelian group has a hamiltonian generating set. Certain classes of nonabelian groups are