On the Chromatic Number of Subsets of the Euclidean Plane
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The chromatic number of a subset of the real plane is the smallest number of colors assigned to the elements of that set such that no two points at distance 1 receive the same color. It is known that the chromatic number of the plane is at least 4 and at most 7. In this note, we determine the bounds on the chromatic number for several classes of subsets of the plane such as extensions of the rational plane, sets in convex position, infinite strips, and parallel lines.
KeywordsChromatic number of the plane Unit distance graph Coloring the plane
Mathematics Subject Classification (1991)Primary 05C12 05C15 05C62 51K99
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