Geodesic
Triviality of function $\omega_2$ for spatial complete graphs
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 51-60

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Let $G_n$, $n\geqslant 6$, be a complete spatial graph with $n$ vertices. In 1983 J. Y. Conway and C. McA. Gordon introduced function $\omega_2$ for all such graphs with 6 vertices. They proved that $\omega_2(G_6) = 1$ for any spatial graph $G_6$, and hence any such graph contains non-trivial link. In present work we prove that $\omega_2(G_n) = 0$ for any spatial complete graph $G_n$ with $n\geqslant 7$ vertices.
Mots-clés : spatial graph
Keywords: hamiltonian set of circles, link, complete graph. 
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     title = {Triviality of function $\omega_2$ for spatial complete graphs},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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A. A. Kazakov; Ph. G. Korablev. Triviality of function $\omega_2$ for spatial complete graphs. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 2, pp. 51-60. http://geodesic.mathdoc.fr/item/VNGU_2013_13_2_a5/