Pancyclic Hamilton cycles in random graphs
β Scribed by C. Cooper
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 466 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0012-365X
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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.
We consider the standard random geometric graph process in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of edge-length. For fixed k β₯ 1, we prove that the first edge in the process that creates a k-connected graph coincides a.a.s. with
## Abstract An __n__βvertex graph is called pancyclic if it contains a cycle of length __t__ for all 3β€__t__β€__n__. In this article, we study pancyclicity of random graphs in the context of resilience, and prove that if __p__>__n__^β1/2^, then the random graph __G__(__n, p__) a.a.s. satisfies the f
## UNIVERSIW OF WATERLOO ' The research reported here has been sponsored by the Canadian Commonwealth Association.