Geodesic
An Approximate Restatement of the Four-Color Theorem
Journal of Graph Algorithms and Applications, Tome 17 (2013) no. 5, pp. 567-573.

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The celebrated Four-Color Theorem was first conjectured in the 1850's. Since then there had been many partial results. More than a century later, it was first proved by Appel and Haken and then subsequently improved by Robertson et al. . These proofs make extensive use of computer for various computations involved. In mathematical community, there continues to be an interest for a proof that is theoretical in nature. Our result provides an interesting restatement of the Four-Color Theorem that requires only approximate colorings. Tait proved in 1880 that the Four-Color Theorem is equivalent to showing that two-edge connected, cubic, planar graphs have edge 3-colorings. Our main result is that this can be weakened to show that if there exists an approximate edge 3-coloring for these graphs, then the Four-Color Theorem is true.
DOI : 10.7155/jgaa.00304
Keywords: graph algorithms, four-color theorem, planar graphs 
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Atish Das Sarma; Amita Gajewar; Richard Lipton; Danupon Nanongkai. An Approximate Restatement of the Four-Color Theorem. Journal of Graph Algorithms and Applications, Tome 17 (2013) no. 5, pp. 567-573. doi : 10.7155/jgaa.00304. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00304/

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