Abstract Let RC( p ) denote the random subgraph of the n -cycle C obtained by selecting or rejecting each of the lines of C with independent probability p or q = 1− p , respectively. By definition RC( p has the same point set as C . The number of lines N in RC( p ) is clearly seen to be a random variable having a binomial probability distribution. The expected value, variance, distribution, and some asymptotic distributions of X j , the number of points in RC( p ) having degree j ( j =0,1,2) are determined. A component of RC( p ) is called big if its order is greater than [ n 2 ]. The probability that RC( p ) will contain a big component is derived. From this it is shown how different choices of p (as a function of n ) effect this probability as n goes to infinity.
[1]
Louis V. Quintas,et al.
Random graphs and the physical world
,
1983
.
[2]
Z. Palka.
On the degrees of vertices in A bichromatic random graph
,
1984
.
[3]
Zbigniew Palka.
On the number of vertices of given degree in a random graph
,
1984,
J. Graph Theory.
[4]
Michal Karonski,et al.
A review of random graphs
,
1982,
J. Graph Theory.
[5]
Béla Bollobás,et al.
Vertices of given degree in a random graph
,
1982,
J. Graph Theory.
[6]
Kai Lai Chung,et al.
A Course in Probability Theory
,
1949
.
[7]
B. Bollobás.
The evolution of random graphs
,
1984
.