On the bigenus of the complete graphs

TL;DR

This paper introduces an infinite family of decompositions of complete graphs into two surface-triangulating graphs, extending known cases and solving a generalized Earth-Moon problem for many surfaces.

Contribution

It presents a new infinite class of biembeddings of complete graphs into orientable surfaces, broadening the scope of known decompositions.

Findings

Infinite family of edge-decompositions into triangulations

Solves a generalized Earth-Moon problem for many surfaces

Extends known cases of complete graph decompositions

Abstract

We describe an infinite family of edge-decompositions of complete graphs into two graphs, each of which triangulate the same orientable surface. Previously, such decompositions had only been known for only a few complete graphs. These so-called biembeddings solve a generalization of the Earth-Moon problem for an infinite number of orientable surfaces.