Index 3 biembeddings of the complete graphs
Combinatorics
2023-01-03 v1
Abstract
We show that the complete graphs on 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.
Keywords
Cite
@article{arxiv.2301.00286,
title = {Index 3 biembeddings of the complete graphs},
author = {Juvenal F. Barajas and Timothy Sun},
journal= {arXiv preprint arXiv:2301.00286},
year = {2023}
}
Comments
8 pages, 4 figures