A Solution to Ringel's Circle Problem
International Symposium on Computational Geometry (SoCG)(2022)
摘要
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.
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关键词
circle problem,ringel,solution
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