Excluded Minors and the Ribbon Graphs of Knots |
| |
Authors: | Iain Moffatt |
| |
Affiliation: | DEPARTMENT OF MATHEMATICS, ROYAL HOLLOWAY UNIVERSITY OF LONDON, EGHAM, SURREY, UNITED KINGDOM |
| |
Abstract: | In this article we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contracting loops is necessary and doing this can create additional vertices and components. Thus, the ribbon graph minor relation is incompatible with the graph minor relation. We discuss excluded minor characterizations of minor closed families of ribbon graphs. Our main result is an excluded minor characterization of the family of ribbon graphs that represent knot and link diagrams. |
| |
Keywords: | embedded graph excluded minor knot link minor ribbon graph |
|
|