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Deciding 4-colorability of planar triangulations

We show, without using the Four Color Theorem, that for each planar triangulation, the number of its proper vertex colorings by 4 colors is a determinant and thus can be calculated in a polynomial time. In particular, we can efficiently decide if the number is non-zero.

preprint2016arXivOpen access
Martin Loebl
math.CODiscrete Mathematics
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Martin Loebl

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