Poussin graph

It is named after Charles Jean de la Vallée-Poussin.

In 1879, Alfred Kempe published a proof of the four color theorem, one of the big conjectures in graph theory.

[1] While the theorem is true, Kempe's proof is incorrect.

Percy John Heawood illustrated it in 1890[2] with a counter-example, and de la Vallée-Poussin reached the same conclusion in 1896 with the Poussin graph.

[3] Kempe's (incorrect) proof is based on alternating chains, and as those chains prove useful in graph theory mathematicians remain interested in such counterexamples.

Tangled Kempe chains in the Poussin graph. The adjacencies between regions of this map form the Poussin graph, partially four-colored with the outer region uncolored. The blue–yellow and blue–green Kempe chains (yellow and green lines) connect the outer region's neighbors, so Kempe would swap colors in the left red–yellow chain and the right red–green chain (red lines), allowing the outer region to be red. As the blue–yellow and blue–green chains cross, this color swap would cause the upper yellow and green regions to both become red, producing an invalid coloring.