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

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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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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AMS subject classification 1980

  • 68 E 99
  • 51 E 10, 05 B 05, 05 C 65