[PDF][PDF] Further biembeddings of twofold triple systems
DM Donovan, TS Griggs, JG Lefevre… - Ars Mathematica …, 2015 - core.ac.uk
DM Donovan, TS Griggs, JG Lefevre, TA McCourt
Ars Mathematica Contemporanea, 2015•core.ac.uk… We construct face two-colourable triangulations of the graph 2Kn in an orientable surface;
equivalently biembeddings of two twofold triple systems of order n, for all n ≡ 16 or 28 (mod
48). The biembeddings come from index 1 current graphs lifted under a group Zn/4 × K4. …
In this paper, for the case n ≡ 28 (mod 48), we give a much simpler construction based on
cyclic biembeddings of Steiner triple systems of order 12m + 7, m ≥ 0. These were found by
Youngs [6] and index 1 current graphs corresponding to these solutions are readily …
equivalently biembeddings of two twofold triple systems of order n, for all n ≡ 16 or 28 (mod
48). The biembeddings come from index 1 current graphs lifted under a group Zn/4 × K4. …
In this paper, for the case n ≡ 28 (mod 48), we give a much simpler construction based on
cyclic biembeddings of Steiner triple systems of order 12m + 7, m ≥ 0. These were found by
Youngs [6] and index 1 current graphs corresponding to these solutions are readily …
Abstract
We construct face two-colourable triangulations of the graph 2Kn in an orientable surface; equivalently biembeddings of two twofold triple systems of order n, for all n≡ 16 or 28 (mod 48). The biembeddings come from index 1 current graphs lifted under a group Zn/4× K4.
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