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Approximate Coloring of Uniform Hypergraphs (Extended Abstract)

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Book cover Algorithms — ESA’ 98 (ESA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1461))

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Abstract

We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of finding the exact value of the chromatic number of a hypergraph is known to be N P-hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r ≥ 3 it is impossible to approximate in polynomial time the chromatic number of r-uniform hypergraphs on n vertices within a factor n 1−∈ for any ∈ > 0, unless N P \( \subseteq \) Z P P. On the positive side, we present an approximation algorithm for coloring r-uniform hypergraphs on n vertices, whose performance ratio is O(n(log log n)2/(log n)2). We also describe an algorithm for coloring 3-uniform 2-colorable hypergraphs on n vertices in Õ(n 9/41) colors, thus improving previous results of Chen and Frieze and of Kelsen, Mahajan and Ramesh.

Research supported by an IAS/DIMACS Postdoctoral Fellowship.

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Author information

Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540

    Michael Krivelevich

  2. Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    Benny Sudakov

Authors
  1. Michael Krivelevich
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  2. Benny Sudakov
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, I-35131, Padova, Italy

    Gianfranco Bilardi  & Geppino Pucci  & 

  2. Department of Electrical Engineering and Computer Science, The University of Illinois at Chicago, 851 South Morgan Street - 1009 SEO, Chicago, IL, 60607-7053, USA

    Gianfranco Bilardi

  3. Dipartimento di Matematica Applicata e Informatica, Università “Cá Foscari” di Venezia, via Torino 155, I-30173, Venezia Mestre, Italy

    Giuseppe F. Italiano

  4. Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, I-35131, Padova, Italy

    Andrea Pietracaprina

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© 1998 Springer-Verlag Berlin Heidelberg

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Krivelevich, M., Sudakov, B. (1998). Approximate Coloring of Uniform Hypergraphs (Extended Abstract). In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_40

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  • DOI: https://doi.org/10.1007/3-540-68530-8_40

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  • Print ISBN: 978-3-540-64848-2

  • Online ISBN: 978-3-540-68530-2

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