On the Seifert graphs of a link diagram and its parallels
Geometric Topology
2013-11-18 v1 Combinatorics
Abstract
Recently, Dasbach, Futer, Kalfagianni, Lin, and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or equivalently, embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon graphs of a knot or link diagram that arise from Seifert states. We provide a characterization of Seifert graphs in terms of Eulerian subgraphs. This characterization can be viewed as a refinement of the fact that Seifert graphs are bipartite. We go on to examine the family of ribbon graphs that arises by forming the parallels of a link diagram and determine how the genus of the ribbon graph of a -fold parallel of a link diagram is related to that of the original link diagram.
Cite
@article{arxiv.1106.4197,
title = {On the Seifert graphs of a link diagram and its parallels},
author = {Stephen Huggett and Iain Moffatt and Natalia Virdee},
journal= {arXiv preprint arXiv:1106.4197},
year = {2013}
}