The Nonexistence of a Decomposition of Complete Graph $K_{12}$ into Three Factors with Diameter Two

Abstract

In this paper we show that the complete graph $K_{12}$ is not decomposable into three factors of diameter two, thus resolving a longstanding open problem. This result completes the solution of decomposition of a complete graph into three
factors, one of which has diameter two and the other factors have finite diameters.