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
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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.
@article{TIMB_2016_24_1_a6,
author = {T. E. Krenkel and T. A. Kulikova},
title = {Three coloring of pure children drawings of snarks and the problem {{\textquotedblleft}The} hunting of the snark{\textquotedblright}},
journal = {Trudy Instituta matematiki},
pages = {47--50},
publisher = {mathdoc},
volume = {24},
number = {1},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMB_2016_24_1_a6/}
}
TY - JOUR AU - T. E. Krenkel AU - T. A. Kulikova TI - Three coloring of pure children drawings of snarks and the problem “The hunting of the snark” JO - Trudy Instituta matematiki PY - 2016 SP - 47 EP - 50 VL - 24 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMB_2016_24_1_a6/ LA - ru ID - TIMB_2016_24_1_a6 ER -
%0 Journal Article %A T. E. Krenkel %A T. A. Kulikova %T Three coloring of pure children drawings of snarks and the problem “The hunting of the snark” %J Trudy Instituta matematiki %D 2016 %P 47-50 %V 24 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMB_2016_24_1_a6/ %G ru %F TIMB_2016_24_1_a6
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/