Abstract
Given a metric space and a set of distances, one constructs the associated distance graph by taking as vertices the points of the space and as edges the pairs whose distance is in the given set. It is a longstanding open question to determine the chromatic number of the graph obtained from the Euclidean plane and a set reduced to one distance. Surprisingly, while many variants of this problem have been studied, only a few non-Euclidean spaces seem to have been seriously considered. In this paper, we consider the planar translation-invariant metrics and the hyperbolic plane. We answer questions of Johnson and Szlam, prove a few other results, and ask many questions.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.