📝 SummarXiv

Abstract

In 1968, Ringel and Youngs solved the remaining cases of the orientable Map Color Theorem by finding genus embeddings of the complete graphs $K_n$, for sufficiently large $n \equiv 2, 8, 11 \pmod{12}$. Following the approach previously explored by the author for $n \equiv 8 \pmod{12}$, we aim to streamline their constructions for $n \equiv 2, 11 \pmod{12}$ by finding families of current graphs with simpler patterns for the arc labelings.