Erdős Problem #130
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the infinite-chromatic subquestion is proved; the rest of the problem remains open
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geometry-topology / Discrete Geometry, Chromatic Number
Erdős Problem #130
For an infinite planar set in strong general position, how large can the chromatic and clique numbers of its positive-integer-distance graph be - in particular, can the chromatic number be infinite? Yes: there is such a set, no three collinear and no four concyclic, with infinite chromatic number.
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For an infinite planar set in strong general position, how large can the chromatic and clique numbers of its positive-integer-distance graph be - in particular, can the chromatic number be infinite? Yes: there is such a set, no three collinear and no four concyclic, with infinite chromatic number.
the infinite-chromatic subquestion is proved; the rest of the problem remains open
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