Index 3 biembeddings of the complete graphs
Juvenal Francisco Barajas, Timothy Sun · arXiv (Cornell University) · 2022
We show that the complete graphs on $24s+21$ vertices have decompositions into two edge-disjoint subgraphs, each of which triangulates an orientable surface. The special case where the two surfaces are homeomorphic solves a generalized Earth-Moon problem for that surface. Unlike previous constructions, these pairs of triangular embeddings are derived from index 3 current graphs.