Abstract
Given a graph in 3-space, in general knotted, can one construct a surface containing the graph in some canonical way so that the embedding of the surface in space, or even the link type of its boundary, is an invariant of the knotted graph? We consider, in particular, surfaces that contain the graph as a spine and that are canonical in the sense of having trivial Seifert linking form. It turns out that θ-curves and K 4-graphs are the unique graphs for which this approach works.
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