Chromatic Number with Several Forbidden Distances in the Space with the ℓ_q-Metric

摘要

We study the chromatic number χ¯ (Xρk) of a metric space X with a metric ρ and k forbidden distances. We obtain an estimate of the form χ¯ (ℝ~nρk) ≥ (Bk) ~(Cn) for cases where the metric ρ on the set ℝ~n is generated by the ℓ_q-norm.