Abstract
The edges of the random graph (with the edge probabilityp=1/2) can be covered usingO(n 2lnlnn/(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)n 2/(2lgn)2.
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Research supported in part by ONR Grant N00014-85K0570 and by NSA/MSP Grant MDA904-90-H-4011.
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Bollobás, B., Erdős, P., Spencer, J. et al. Clique coverings of the edges of a random graph. Combinatorica 13, 1–5 (1993). https://doi.org/10.1007/BF01202786
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DOI: https://doi.org/10.1007/BF01202786