## Abstract In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Ξ is __n__β__HCβextendable__ if it contains a path of length __n__ and if every such path is contained in some Hamilton cycle of Ξ. Similarly, Ξ is __weakly n__β__HPβ
Hamilton paths in Cayley diagraphs of metacyclic groups
β Scribed by Stephen J. Curran
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 480 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We obtain a characterization of all Hamilton paths in the Cayley digraph of a metacyclic group G with generating set {x, y} where (yx-') a G. The abundance of these Hamilton paths allows us to show that Hamilton paths occur in groups of at least two.
π SIMILAR VOLUMES
The Hamilton cycles of a graph generate a subspace of the cycle space called the Hamilton space. The Hamilton space of any connected Cayley graph on an abelian group is determined in this paper.
We show every finitely-generated, infinite abeliar\_ group (i.e. Zn x G where G is a finite abelian group) has a minimal generating set for which the Cayley digraph has a two-way in&rite hamiltonian path, and if n 2 2, then this Cayley digraph also has a one-way infinite hamiltonian path. We show fu