Geodesic
Three coloring of pure children drawings of snarks and the problem “The hunting of the snark”
Trudy Instituta matematiki, Tome 24 (2016) no. 1, pp. 47-50.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Tait theorem as a consequence of Four Color Theorem states that planar qubic graphs are edge three-colorable. The first graph which is a counterexample for the Tait theorem was a nontrivial qubic (trivalent) Petersen graph $P,$ which is the only and minimal graph with chromatic index 4. The integer sequence OEIS A130315 describes (as defined by Martin Gardner) the number of (with girth $\ge5$) snarks, that are nontrivial qubic graphs with $2n$ verticies. The conjecture is presented that via transition from category Snarks to category SnarksPureDessins the derived two-colored graphs (pure children drawings of snarks) can be three-colored at halfedges. The embedding of the Petersen graph in double torus $\Sigma_2$ is presented. The $RGB$ theorem about the cycle double cover of the Peterson-Belyi graph $PB$ is proved. 
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T. E. Krenkel; T. A. Kulikova. Three coloring of pure children drawings of snarks and the problem “The hunting of the snark”. Trudy Instituta matematiki, Tome 24 (2016) no. 1, pp. 47-50. http://geodesic.mathdoc.fr/item/TIMB_2016_24_1_a6/

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