Let H(n, p) denote the size of the largest induced cycle in a random graph C(n, p). It is shown that if the expected average degree of G(n, p) is a constant larger than 1, then H(n, p) is of the order n with probability 1 -o(l). Moreover, for C(n, p) with large average degree, H(n, p) is determined
On the Largest Component of the Random Graph at a Nearcritical Stage
β Scribed by Boris Pittel
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 225 KB
- Volume
- 82
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
The random graphs G(n, Pr(edge)= p), G(n, *edges=M) at the critical range p=(1+*n &1Γ3 )Γn and M=(nΓ2)(1+*n &1Γ3 ) are studied. The limiting distribution of the largest component size is determined.
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