We consider the random poset P(n, p) which is generated by first selecting each subset of [n]=[1, ..., n] with probability p and then ordering the selected subsets by inclusion. We give asymptotic estimates of the size of the maximum antichain for arbitrary p= p(n). In particular, we prove that if p
โฆ LIBER โฆ
The largest super-increasing subset of a random set
โ Scribed by Karnin, E.; Hellman, M.
- Book ID
- 114635224
- Publisher
- IEEE
- Year
- 1983
- Tongue
- English
- Weight
- 408 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0018-9448
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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