Consider the collection of edge bicolorings of a graph that are cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and reversing colors around a vertex. In the case of the plane, this is well studied, but for other surfaces, the computation is more subtle. While this question can be stated purely graph theoretically, it has interesting applications in knot theory.
Classification :
05C10
Mots-clés :
embedded graphs, checkerboard graphs, knot theory, region crossing change, cycle and cocycle spaces of graphs, graphs on the torus
Affiliations des auteurs :
Oliver T. Dasbach
1
;
Heather M. Russell
2
1
Louisiana State University
2
University of Richmond
@article{10_37236_7384,
author = {Oliver T. Dasbach and Heather M. Russell},
title = {Equivalence of edge bicolored graphs on surfaces},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/7384},
zbl = {1397.57024},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7384/}
}
TY - JOUR
AU - Oliver T. Dasbach
AU - Heather M. Russell
TI - Equivalence of edge bicolored graphs on surfaces
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/7384/
DO - 10.37236/7384
ID - 10_37236_7384
ER -
%0 Journal Article
%A Oliver T. Dasbach
%A Heather M. Russell
%T Equivalence of edge bicolored graphs on surfaces
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/7384/
%R 10.37236/7384
%F 10_37236_7384
Oliver T. Dasbach; Heather M. Russell. Equivalence of edge bicolored graphs on surfaces. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7384
