If $\mathrm{\Gamma }$ is a closed Noetherian graph on a $\sigma$-compact Polish space with no infinite cliques, it is consistent with the choiceless set theory ZF$$$+$$$DC that $\mathrm{\Gamma }$ is countably chromatic and there is no Vitali set.

中文翻译：

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着色封闭的诺特图

如果$\mathrm{\gamma }$是一个闭诺特图$\sigma$- 紧波兰空间，没有无限派系，与无选择集合论ZF一致$$$+$$$直流那个$\mathrm{\gamma }$是可数半音阶并且没有维塔利集。