Abstract
In 1999, at one of his last public lectures, Tutte discussed a question he had considered since the times of the Four Color Conjecture. He asked whether the 4-coloring complex of a planar triangulation could have two components in which all colorings had the same parity. In this note we answer Tutte’s question contrary to his speculations by showing that there are triangulations of the plane whose coloring complexes have arbitrarily many even and odd components.
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