Battle, Harary, and Kodama (1962) and independently Tutte (1963) proved that the complete graph with nine vertices is not biplanar. Aiming towards simplicity and brevity, in this note we provide a short proof of this claim.

中文翻译：

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$K_9$ 非双平面性的简短证明

Battle、Harary 和 Kodama (1962) 以及 Tutte (1963) 独立证明了具有九个顶点的完整图不是双平面的。为了简单和简洁，在本说明中，我们提供了这一主张的简短证明。