A short proof of the non-biplanarity of $K_9$

Abstract

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.

arXiv commentAppears in the Proceedings of the 29th International Symposium on Graph Drawing and Network Visualization (GD 2021)