References of "Petit, Camille"
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See detailChromatic numbers for the hyperbolic plane and discrete analogs
Parlier, Hugo UL; Petit, Camille

E-print/Working paper (2017)

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 ... [more ▼]

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. [less ▲]

Detailed reference viewed: 38 (5 UL)
Full Text
Peer Reviewed
See detailChromatic numbers of hyperbolic surfaces
Parlier, Hugo UL; Petit, Camille

in Indiana Univ. Math. J. (2016), 65(4), 1401--1423

Detailed reference viewed: 123 (3 UL)