Coloring Semirandom Graphs Optimally

  • Amin Coja-Oghlan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)


We present heuristics and algorithms with polynomial expected running time for coloring semirandom k-colorable graphs made up as follows. Partition the vertex set V={1,...,n} into k classes V 1,...,V k randomly and include each V i -V j -edge \((i\not=j)\) with probability p independently. Then, an adversary adds further V i -V j -edges \((i\not=j)\). We show that if np ≥ max {(1 + ε)kln (n),Ck 2}, an optimal coloring can be found in polynomial time with high probability. Furthermore, if np ≥ C max {kln (n),k 2ln (k)}, an optimal coloring can be found in polynomial expected time. By contrast, it is NP-hard to find a k-coloring whp. if \(np\leq(\frac12-\varepsilon)k\ln(n/k)\).


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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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

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