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On the algorithmic complexity of coloring simple hypergraphs and steiner triple systems

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Abstract

In this paper we establish that decidingt-colorability for a simplek-graph whent≧3,k≧3 is NP-complete. Next, we establish that if there is a polynomial time algorithm for finding the chromatic number of a Steiner Triple system then there exists a polynomial time “approximation” algorithm for the chromatic number of simple 3-graphs. Finally, we show that the existence of such an approximation algorithm would imply that P=NP.

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Authors and Affiliations

  1. Department of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

    Kevin T. Phelps

  2. FJFI ČVUT Department of Mathematics, Husova 5, Praha 1, Czechoslovakia

    Vojtěch Rödl

Authors
  1. Kevin T. Phelps
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  2. Vojtěch Rödl
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Dedicated to Paul Erdős on his seventieth birthday

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Phelps, K.T., Rödl, V. On the algorithmic complexity of coloring simple hypergraphs and steiner triple systems. Combinatorica 4, 79–88 (1984). https://doi.org/10.1007/BF02579160

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  • DOI: https://doi.org/10.1007/BF02579160

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