Biembedding Steiner Triple Systems and n-cycle Systems on Orientable Surfaces
Combinatorics
2015-05-18 v1
Abstract
In 2015, Archdeacon introduced the notion of Heffter arrays and showed the connection between Heffter arrays and biembedding m-cycle and an n-cycle systems on a surface. In this paper we exploit this connection and prove that for every n >= 3 there exists an orientable embedding of the complete graph on 6n+1 vertices with each edge on both a 3-cycle and an -cycle. We also give an analogous (but partial) result for biembedding a 5-cycle system and an n-cycle system.
Cite
@article{arxiv.1505.04070,
title = {Biembedding Steiner Triple Systems and n-cycle Systems on Orientable Surfaces},
author = {Jeffrey H. Dinitz and Amelia R. W. Mattern},
journal= {arXiv preprint arXiv:1505.04070},
year = {2015}
}