The edges of the random graph (with the edge probabilityp=1/2) can be covered usingO(n2lnlnn/(lnn)2) cliques. Hence this is an upper bound on the intersection number (also called clique cover number) of the random graph. A lower bound, obtained by counting arguments, is (1−ɛ)n2/(2lgn)2.
AMS subject classification code (1991)05 C 80
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