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Coloring Semirandom Graphs Optimally

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Automata, Languages and Programming (ICALP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3142))

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Abstract

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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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Amin Coja-Oghlan

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  1. Amin Coja-Oghlan
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Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. Department of Mathematics, University of Turku, Turku, Finland

    Arto Lepistö

  4. Laboratory for Foundations of Computer Science, University of Edinburgh,  

    Donald Sannella

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© 2004 Springer-Verlag Berlin Heidelberg

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Coja-Oghlan, A. (2004). Coloring Semirandom Graphs Optimally. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_34

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  • DOI: https://doi.org/10.1007/978-3-540-27836-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

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