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Combinatorica

, Volume 4, Issue 1, pp 79–88 | Cite as

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

  • Kevin T. Phelps
  • Vojtěch Rödl
Article

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.

AMS subject classification 1980

68 E 99 51 E 10, 05 B 05, 05 C 65 

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Copyright information

© Akadémiai Kiadó 1984

Authors and Affiliations

  • Kevin T. Phelps
    • 1
  • Vojtěch Rödl
    • 2
  1. 1.Department of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.FJFI ČVUT Department of MathematicsPraha 1Czechoslovakia

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