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.

翻译：哈拉里和科达马(Harary,1962年)和科达马(Kodama,以及独立的图特(Tutte,1963年)证明,带有九面顶的完整图表不是双平面的。 为了简单和简洁,我们在本照会中提供了这一说法的简短证据。