On the bigenus of the complete graphs
Combinatorics
2021-11-24 v1
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.
Cite
@article{arxiv.2111.11671,
title = {On the bigenus of the complete graphs},
author = {Timothy Sun},
journal= {arXiv preprint arXiv:2111.11671},
year = {2021}
}
Comments
8 pages, 2 figures