Geodesic
Heffter arrays and biembedding graphs on surfaces
Dan Archdeacon1
1The University of Vermont
The electronic journal of combinatorics, Tome 22 (2015) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

A Heffter array is an $m \times n$ matrix with nonzero entries from $\mathbb{Z}_{2mn+1}$ such that i) every row and column sum to 0, and ii) exactly one of each pair $\{x,-x\}$ of nonzero elements appears in the array. We construct some Heffter arrays. These arrays are used to build current graphs used in topological graph theory. In turn, the current graphs are used to embed the complete graph $K_{2mn+1}$ so that the faces can be 2-colored, called a biembedding. Under certain conditions each color class forms a cycle system. These generalize biembeddings of Steiner triple systems. We discuss some variations including Heffter arrays with empty cells, embeddings on nonorientable surfaces, complete multigraphs, and using integer arithmetic in place of modular arithmetic.
DOI : 10.37236/4874
Classification : 05C60, 05C15
Mots-clés : biembeddings, current graphs

Dan Archdeacon  1

1 The University of Vermont 
@article{10_37236_4874,
     author = {Dan Archdeacon},
     title = {Heffter arrays and biembedding graphs on surfaces},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {1},
     doi = {10.37236/4874},
     zbl = {1310.05142},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4874/}
}
TY  - JOUR
AU  - Dan Archdeacon
TI  - Heffter arrays and biembedding graphs on surfaces
JO  - The electronic journal of combinatorics
PY  - 2015
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/4874/
DO  - 10.37236/4874
ID  - 10_37236_4874
ER  - 
%0 Journal Article
%A Dan Archdeacon
%T Heffter arrays and biembedding graphs on surfaces
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4874/
%R 10.37236/4874
%F 10_37236_4874
Dan Archdeacon. Heffter arrays and biembedding graphs on surfaces. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4874

Cité par Sources :