Sparse Quasi-Random Graphs
β Scribed by Fan Chung; Ronald Graham
- Publisher
- Springer-Verlag
- Year
- 2002
- Tongue
- English
- Weight
- 322 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0209-9683
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## Abstract In this article we study Hamilton cycles in sparse pseudoβrandom graphs. We prove that if the second largest absolute value Ξ» of an eigenvalue of a __d__βregular graph __G__ on __n__ vertices satisfies and __n__ is large enough, then __G__ is Hamiltonian. We also show how our main resu
We consider the diameter of a random graph G n p for various ranges of p close to the phase transition point for connectivity. For a disconnected graph G, we use the convention that the diameter of G is the maximum diameter of its connected components. We show that almost surely the diameter of rand