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.

翻译：我们构筑飞机圆圈的圆圈, 使得它们的相貌图图中任意出现大圆圈和色子数。 这为Ringel圆圈问题(1959年)提供了强烈的否定答案。 证据依据的是一个(多维)版本的加莱定理,其中含有多面性限制, 我们来自Hales- Jewett定理, 可能具有独立的利益。