1Department of Mathematics and Statistics The Open University 2Heilbronn Institute for Mathematical Research School of Mathematics University of Bristol
The electronic journal of combinatorics, Tome 21 (2014) no. 1
For all $m\geq 1$ and $k\geq 2$, we construct closed 2-cell embeddings of the complete graph $K_{8km+4k+1}$ with faces of size $4k$ in orientable surfaces. Moreover, we show that when $k\geq 3$ there are at least $(2m-1)!/2(2m+1)=2^{2m\text{log}_2m-\mathrm{O}(m)}$ nonisomorphic embeddings of this type. We also show that when $k=2$ there are at least $\frac14 \pi^{\frac12}m^{-\frac{5}{4}}\left(\frac{4m}{e^2}\right)^{\sqrt{m}}(1-\mathrm{o}(1))$ nonisomorphic embeddings of this type.
1
Department of Mathematics and Statistics
The Open University
2
Heilbronn Institute for Mathematical Research
School of Mathematics
University of Bristol
@article{10_37236_3189,
author = {Mike J Grannell and Thomas A McCourt},
title = {Doubly even orientable closed 2-cell embeddings of the complete graph},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/3189},
zbl = {1300.05180},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3189/}
}
TY - JOUR
AU - Mike J Grannell
AU - Thomas A McCourt
TI - Doubly even orientable closed 2-cell embeddings of the complete graph
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3189/
DO - 10.37236/3189
ID - 10_37236_3189
ER -
%0 Journal Article
%A Mike J Grannell
%A Thomas A McCourt
%T Doubly even orientable closed 2-cell embeddings of the complete graph
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3189/
%R 10.37236/3189
%F 10_37236_3189
Mike J Grannell; Thomas A McCourt. Doubly even orientable closed 2-cell embeddings of the complete graph. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3189
