Geodesic
On the Chromatic Number for a Set of Metric Spaces
Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 422-431

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We study the problem of finding the chromatic number of a metric space with a forbidden distance. Using the linear-algebraic technique in combinatorics and convex optimization methods, we obtain a set of new estimates and observe the change of the asymptotic lower bound for the chromatic number of Euclidean space under the continuous change of the metric from $l_1$ to $l_2$.
Keywords: metric space with a forbidden distance, chromatic number, convex optimization, Euclidean space, graph, Karush–Kuhn–Tucker theorem, Lagrange function. 
@article{MZM_2012_91_3_a8,
     author = {I. M. Mitricheva (Shitova)},
     title = {On the {Chromatic} {Number} for a {Set} of {Metric} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {422--431},
     publisher = {mathdoc},
     volume = {91},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a8/}
}
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I. M. Mitricheva (Shitova). On the Chromatic Number for a Set of Metric Spaces. Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 422-431. http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a8/