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Chromatic numbers for the hyperbolic plane and discrete analogs

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 نشر من قبل Hugo Parlier
 تاريخ النشر 2017
  مجال البحث
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We study colorings of the hyperbolic plane, analogously to the Hadwiger-Nelson problem for the Euclidean plane. The idea is to color points using the minimum number of colors such that no two points at distance exactly $d$ are of the same color. The problem depends on $d$ and, following a strategy of Kloeckner, we show linear upper bounds on the necessary number of colors. In parallel, we study the same problem on $q$-regular trees and show analogous results. For both settings, we also consider a variant which consists in replacing $d$ with an interval of distances.



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