Thin position and planar surfaces for graphs in the 3-sphere
Abstract
Description
We show that given a trivalent graph in $S^3$, either the graph complement contains an essential almost meridional planar surface or thin position for the graph is also bridge position. This can be viewed as an extension of a theorem of Thompson to graphs. It follows that any graph complement always contains a useful planar surface.
7 pages, 1 figure
7 pages, 1 figure