Elsevier

Discrete Mathematics

Volume 313, Issue 7, 6 April 2013, Pages 872-885
Discrete Mathematics

On small subgraphs in a random intersection digraph

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Abstract

Given a set of vertices V and a set of attributes W let each vertex vV include an attribute wW into a set S(v) with probability p and let it include w into a set S+(v) with probability p+ independently for each wW. The random binomial intersection digraph on the vertex set V is defined as follows: for each u,vV the arc uv is present if S(u) and S+(v) are not disjoint. For any h=2,3, we determine the birth threshold of the complete digraph on h vertices and describe the configurations of intersecting sets that realise the threshold.

Keywords

Digraph
Clique
Threshold
Random intersection graph

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