Geodesic
Distance graphs having large chromatic numbers and containing no cliques or cycles of a~given size
Sbornik. Mathematics, Tome 204 (2013) no. 4, pp. 508-538

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

It is established that there exist sequences of distance graphs $G_n\subset\mathbb R^n$, with chromatic numbers which grow exponentially, but, at the same time, without cliques or cycles of a given size. Bibliography: 42 titles.
Keywords: distance graph, random graph, chromatic number, cycle.
Mots-clés : clique 
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     title = {Distance graphs having large chromatic numbers and containing no cliques or cycles of a~given size},
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E. E. Demekhin; A. M. Raigorodskii; O. I. Rubanov. Distance graphs having large chromatic numbers and containing no cliques or cycles of a~given size. Sbornik. Mathematics, Tome 204 (2013) no. 4, pp. 508-538. http://geodesic.mathdoc.fr/item/SM_2013_204_4_a2/