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.

中文翻译：

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威廉·T·图特的最后一次诱惑

1999年，在他最后一次公开演讲中，Tutte讨论了自四色猜想时代以来他所考虑的问题。他询问平面三角剖分的4色复合体是否可以具有两个成分，其中所有颜色都具有相同的奇偶性。在此注释中，我们通过显示平面的三角剖分中的着色复合物具有任意多的偶数和奇数分量来回答与Tutte的推测相反的问题。