Kittel, Errera, and Soifer showed that Kempe chains can be tangled, disproving one erroneous proof of this.
A generalization of this result involves edge contractions and is named after Hugo Hadwiger. Kittel, Errera, and Soifer showed that Kempe chains can be tangled, disproving one erroneous proof of this. Its generalization, called the Heawood conjecture, contains the floor function and could not be proven necessary and sufficient for cases of genus 0, necessitating a separate proof of this. A crossed-prism graph can show that it does not hold for a torus. Its proof, demonstrated by Appel and Hakan, involved 1,936 configurations, each reduced to a smaller graph, then checked with a computer. For 10 points, name this theorem stating the chromatic number needed to draw a map.
A generalization of this result involves edge contractions and is named after Hugo Hadwiger.
{four}-{color} (map) theorem or {Guthrie's problem}