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
Holes in random graphs
✍ Scribed by Tomasz Łuczak
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 376 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
tuczak, T., Cycles in random graphs, Discrete Mathematics 98 (1991) 231-236. Let G(n, p) be a graph on n vertices in which each possible edge is presented independently with probability p = p(n) and u'(n, p) denote the number of vertices of degree 1 in G(n, p). It is shown that if E > 0 and rip(n)))
For each fixed p, the random directed graph D(n, p) on n vertices with (directed) edge probability p possesses a kernel with probability tending to 1 as n + a. Pour chaque p fixe, le graphe alCatoire D(n, p) a n sommets et probabilitts des arcs Cgales B p posstde un noyau avec une probabilit6 tenda