Covering the edges of a random graph by cliques

Alan Frieze; Bruce Reed

Covering the edges of a random graph by cliques

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arxiv 1103.4870 v1 pith:SX52WT53 submitted 2011-03-24 math.CO

Alan Frieze , Bruce Reed This is my paper · ORCID

classification math.CO

keywords graphnumbercliquecliquescoveredgesrandomconsider

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The clique cover number of a graph G is the minimum number of cliques required to cover the edges of graph G. In this paper we consider the random graph G(n,p), for p constant. We prove that with probability 1-o(1), the clique number of G(n,p) is Theta(n^2/\log^2n).

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Asymptotically Smaller Encodings for Graph Problems and Scheduling
cs.LO 2025-06 conditional novelty 7.0 of 10

Independent set, vertex cover, k-coloring and clique admit CNF encodings with O(n^2/log n) clauses, and the disjoint-intervals encoding needs only O(n^2 log n) clauses.

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