On the independence number of random graphs

On the independence number of random graphs

On the b-Independence Number of Sparse Random Graphs

Let graph G = (V,E) and integer b ≥ 1 be given. A set S ⊆ V is said to be b-independent if u, v ∈ S implies dG(u, v) > b where dG(u, v) is the shortest distance between u and v in G. The b-independence number αb(G) is the size of the largest b-independent subset of G. When b = 1 this reduces to the standard definition of independence number. We study this parameter in relation to the random gra...

On The Independence Number Of Random Interval Graphs

A random interval graph of order n is generated by picking 2n numbers X 1 : : : X 2n independently from the uniform distribution on 0; 1] and considering the collection of n intervals with extremities X 2i?1 and X 2i for i 2 f1;:::ng. The graph vertices correspond to intervals. Two vertices are connected if the corresponding intervals intersect. This paper characterizes the uctuations of the in...

On the Independence Number of Random Cubic Graphs

We show that as n —> oo, the independence number c*(G), for almost all 3-regular graphs G on n vertices, is at least (61og(3/2) — 2 — e)n, for any constant e > 0. We prove this by analyzing a greedy algorithm for finding independent sets.

On the k-independence number in graphs

For an integer k ≥ 1 and a graph G = (V,E), a subset S of V is kindependent if every vertex in S has at most k − 1 neighbors in S. The k-independent number βk(G) is the maximum cardinality of a kindependent set of G. In this work, we study relations between βk(G), βj(G) and the domination number γ(G) in a graph G where 1 ≤ j < k. Also we give some characterizations of extremal graphs.