On the hardness of 4-coloring a 3-collorable graph

@article{Guruswami2000OnTH,
  title={On the hardness of 4-coloring a 3-collorable graph},
  author={Venkatesan Guruswami and Sanjeev Khanna},
  journal={Proceedings 15th Annual IEEE Conference on Computational Complexity},
  year={2000},
  pages={188-197}
}
  • V. Guruswami, S. Khanna
  • Published 4 July 2000
  • Mathematics, Computer Science
  • Proceedings 15th Annual IEEE Conference on Computational Complexity
We give a new proof showing that it is NP-hard to color a 3-colorable graph using just four colors. This result is already known, but our proof is novel as it does not rely on the PCP theorem. This highlights a qualitative difference between the known hardness result for coloring 3-colorable graphs and the factor n/sup /spl epsiv// hardness for approximating the chromatic number of general graphs, as the latter result is known to imply (some form of) PCP theorem. Another aspect in which our… 
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