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- W2078703014 abstract "We investigate k -colorings of the rational n -space, Q n , such that any two points at distance one get distinct colors. Two types of colorings are considered: patch colorings where the colors occupy open sets with parts of their boundary, and rigid colorings which uniquely extend from any open subset of Q n . We prove that the existence of a patch k -coloring of Q n implies the existence of a k -coloring of R n . We show that every 2-coloring of Q 2 or Q 3 , and every 4-coloring of Q 4 is rigid. We also construct a rigid 3-coloring of Q 2 ." @default.
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- W2078703014 date "2002-01-01" @default.
- W2078703014 modified "2023-10-17" @default.
- W2078703014 title "Patch Colorings and Rigid Colorings of the Rational n-Space" @default.
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- W2078703014 doi "https://doi.org/10.1006/jctb.2001.2062" @default.
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