This paper proves that every planar graph G contains a matching M such that the Alon-Tarsi number of $G-M$ is at most 4. As a consequence, $G-M$ is 4-paintable, and hence G itself is 1-defective 4-paintable. This improves a result of Cushing and Kierstead (2010) [5], who proved that every planar graph is 1-defective 4-choosable.

中文翻译：

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平面图的Alon-Tarsi数减去匹配项

本文证明了每个平面图G都包含一个匹配M使得Alon-Tarsi数为$G-\mathrm{中号}$ 最多为4。因此， $G-\mathrm{中号}$是4画图的，因此G本身是1缺陷的4画图。这改善了Cushing和Kierstead（2010）的结果[5]，他们证明了每个平面图都是1缺陷4选择的。