## Abstract A cycle __C__ in a graph __G__ is a __Hamilton cycle__ if __C__ contains every vertex of __G__. Similarly, a path __P__ in __G__ is a __Hamilton path__ if __P__ contains every vertex of __G__. We say that __G__ is __Hamilton__β__connected__ if for any pair of vertices, __u__ and __v__ o
Approximately Counting Hamilton Paths and Cycles in Dense Graphs
β Scribed by Dyer, Martin; Frieze, Alan; Jerrum, Mark
- Book ID
- 118178133
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1998
- Tongue
- English
- Weight
- 265 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0097-5397
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G be chosen uniformly at random from the set G G r, n of r-regular graphs w x Ε½ . with vertex set n . We describe polynomial time algorithms that whp i find a Ε½ . Hamilton cycle in G, and ii approximately count the number of Hamilton cycles in G.
## 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