Author:
Dasbach Oliver T.,Russell Heather M.
Abstract
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.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
3 articles.
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1. Region crossing change on surfaces;Mathematische Zeitschrift;2021-09-30
2. The multi-region index of a knot;Journal of Knot Theory and Its Ramifications;2020-03-19
3. Ineffective sets and the region crossing change operation;Journal of Knot Theory and Its Ramifications;2020-02-25