Given a cycle with n nodes a random subgraph is created by 'accepting' edges with probability p and 'rejecting' them with probability q = 1 -p. The parameter of interest is the order of the largest component. There are some partial answers to this question in the literature. Using an appropriate enc
The largest component in a random subgraph of the n-cycle
โ Scribed by Gyula O.H. Katona; Louis V. Quintas
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 214 KB
- Volume
- 121
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The random graphs G(n, Pr(edge)= p), G(n, \*edges=M) at the critical range p=(1+\*n &1ร3 )รn and M=(nร2)(1+\*n &1ร3 ) are studied. The limiting distribution of the largest component size is determined.
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
We consider two types of random subgraphs of the n-cube. For these models we study the asymptotic behaviour of the number of d-cubes when d = 1,2,
A random tournament T is obtained by independently orienting the edges of n 1 the complete graph on n vertices, with probability for each direction. We study the 2 asymptotic distribution, as n tends to infinity, of a suitable normalization of the number of subgraphs of T that are isomorphic to a gi
The author proved that, for c > 1, the random graph G(n, p ) on n vertices with edge probability p = c / n contains almost always an induced tree on at least q n ( 1 -o( 1)) vertices, where L Y ~ is the positive root of the equation CLY = log( 1 + c'a). It is shown here that if c is sufficiently lar