English

Index 3 biembeddings of the complete graphs

Combinatorics 2023-01-03 v1

Abstract

We show that the complete graphs on 24s+2124s+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.

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