Abstract:
We study the chromatic number ¯χ(X;ρ;k)¯¯¯¯χ(X;ρ;k) of a metric space XX with a metric ρρ and kk forbidden distances. We obtain an estimate of the form ¯χ(Rn;ρ;k)≥(Bk)Cn¯¯¯¯χ(Rn;ρ;k)≥(Bk)Cn for cases where the metric ρρ on the set Rn is generated by the ℓq-norm.
Citation:
A. V. Berdnikov, “Chromatic number with several forbidden distances in the space with the ℓq-metric”, Contemporary Mathematics and Its Applications, 100 (2016), 12–18; Journal of Mathematical Sciences, 227:4 (2017), 395–401
\Bibitem{Ber16}
\by A.~V.~Berdnikov
\paper Chromatic number with several forbidden distances in the space with the ~$\ell_q$-metric
\jour Contemporary Mathematics and Its Applications
\yr 2016
\vol 100
\pages 12--18
\mathnet{http://mi.mathnet.ru/cma403}
\transl
\jour Journal of Mathematical Sciences
\yr 2017
\vol 227
\issue 4
\pages 395--401
\crossref{https://doi.org/10.1007/s10958-017-3592-0}
Linking options:
https://www.mathnet.ru/eng/cma403
https://www.mathnet.ru/eng/cma/v100/p12
This publication is cited in the following 3 articles:
Eric Naslund, “The chromatic number of RnRn with multiple forbidden distances”, Mathematika, 69:3 (2023), 692
L. I. Bogolubsky, A. M. Raigorodskii, “A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics ℓ1 and ℓ2”, Math. Notes, 105:2 (2019), 180–203
A. V. Bobu, A. E. Kupriyanov, “Refinement of Lower Bounds of the Chromatic Number of a Space with Forbidden One-Color Triangles”, Math. Notes, 105:3 (2019), 329–341
Citation in format AMSBIB
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