On Radial Colorings of Annuli
Jeremy F. Alm, Jacob Manske
TL;DR
This paper investigates the minimum number of colors needed to color points in annuli so that no two points at a unit distance share the same color, focusing on radial colorings and determining their chromatic numbers.
Contribution
The paper completely determines the radial chromatic numbers of various annuli, providing new insights into coloring problems in geometric graph theory.
Findings
Radial chromatic numbers of various annuli are explicitly determined.
Radial colorings are characterized as 'nice' colorings in the context of annuli.
The study advances understanding of unit-distance graph colorings in geometric settings.
Abstract
We consider the chromatic numbers of unit-distance graphs of various annuli. In particular, we consider radial colorings, which are "nice" colorings, and completely determine the radial chromatic numbers of various annuli.
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Taxonomy
Topicsgraph theory and CDMA systems