# 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} }

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…

## 26 Citations

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