A solution to Ringel's circle problem

James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, Bartosz Walczak

Research output: Working paper/PreprintPreprint

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We construct families of circles in the plane such that their tangency graphs have arbitrarily large girth and chromatic number. This provides a strong negative answer to Ringel's circle problem (1959). The proof relies on a (multidimensional) version of Gallai's theorem with polynomial constraints, which we derive from the Hales-Jewett theorem and which may be of independent interest.
Original languageEnglish
StatePublished - 9 Dec 2021


  • math.CO
  • cs.DM


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