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
Size of largest and second largest cluster in random percolation
β Scribed by A. Margolina; H.J. Herrmann; D. Stauffer
- Book ID
- 107986163
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 258 KB
- Volume
- 93
- Category
- Article
- ISSN
- 0375-9601
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider four families of forests on n vertices: labeled and unlabeled forests containing rooted and unrooted trees, respectively. A forest is chosen uniformly from one of the given four families. The limiting distribution of the size of its largest tree is then studied as n Βͺ Ο±. Convergences to
## Abstract We produce in this paper an upper bound for the number of vertices existing in a clique of maximum cardinal. The proof is based in particular on the existence of a maximum cardinal clique that contains no vertex __x__ such that the neighborhood of __x__ is contained in the neighborhood
## Abstract A graph is point determining if distinct vertices have distinct neighborhoods. The nucleus of a pointβdetermining graph is the set __G__^O^ of all vertices, __v__, such that __G__β__v__ is point determining. In this paper we show that the size, Ο(__G__), of a maximum clique in __G__ sat