The List-Chromatic Number of Infinite Graphs Defined on Euclidean Spaces

Abstract

If D is a countable set of positive reals, 2 ≤ n < ω, let Xn(D) be the graph with the points of R as vertices where two vertices are joined iff their distance is in D. We determine the list-chromatic number of Xn(D) as much as possible. 
DOI: 10.1007/s00454-009-9228-5

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