Poussin graph

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Poussin graph

Vertices	15
Edges	39
Radius	3
Diameter	3
Girth	3
Automorphisms	2 (Z/2Z)
Chromatic number	4
Chromatic index	6
Properties	Hamiltonian Planar
Table of graphs and parameters

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.

In graph theory, the Poussin graph is a planar graph with 15 vertices and 39 edges. It is named after Charles Jean de la Vallée-Poussin.

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