Vertex-cover in random graphs with small connectivity: an exact solution

Abstract

We consider the vertex-cover problem on a finite-connectivity random graph with N vertices and connectivity c. For c smaller than 1/e, we prove that the cardinality of the minimal vertex cover is given by [1 W(c)(2 + W(c))/ 2 c] N + o(N), where W is the Lambert W function, as obtained by Hartmann and Weigt, [1], using the replica approach. The result is… (More)

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Cite this paper

@inproceedings{Caglioti2008VertexcoverIR, title={Vertex-cover in random graphs with small connectivity: an exact solution}, author={Emanuele Caglioti}, year={2008} }