Abstract
The Unit-Distance Graph problem in Euclidean plane asks for the minimum number of colors, so that each point on the Euclidean plane can be assigned a single color with the condition that the points at unit distance apart are assigned different colors. It is well known that this number is between 4 and 7, but the exact value is not known. Here this problem is generalized to Minkowski metric spaces and once again the answer is shown to be between 4 and 7. In extreme special cases where the unit circle is a parallelogram or a hexagon the answer is shown to be exactly 4.
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References
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Chilakamarri, K.B. Unit-distance graphs in Minkowski metric spaces. Geom Dedicata 37, 345–356 (1991). https://doi.org/10.1007/BF00181411
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DOI: https://doi.org/10.1007/BF00181411