%0 Journal Article
%T On the Seifert graphs of a link diagram and its parallels
%A Stephen Huggett
%A Iain Moffatt
%A Natalia Virdee
%J Mathematics
%D 2011
%I arXiv
%R 10.1017/S0305004112000102
%X 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 $r$-fold parallel of a link diagram is related to that of the original link diagram.
%U http://arxiv.org/abs/1106.4197v1