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Abstract

We study the Lovász number ϑ along with two further SDP relaxations ϑ 1/2, ϑ 2 of the independence number and the corresponding relaxations \(\bar\vartheta\), \(\bar\vartheta_{1/2}\), \(\bar\vartheta_2\) of the chromatic number on random graphs G n, p . We prove that \(\bar\vartheta,\bar\vartheta_{1/2},\bar\vartheta_2(G_{n,p})\) in the case p<n  − 1/2 −  ε are concentrated in intervals of constant length. Moreover, we estimate the probable value of \(\vartheta,\bar\vartheta(G_{n,p})\) etc. for essentially the entire range of edge probabilities p. As applications, we give improved algorithms for approximating α(G n, p ) and for deciding k-colorability in polynomial expected time.

Keywords

Random Graph Chromatic Number Vertex Cover Input Graph Independence Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Amin Coja-Oghlan
    • 1
  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany

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