Sewing Ribbons on Graphs in Space

Dan Archdeacon, Paul Bonnington, Bruce Richter, and Jozef Siran


An {em open ribbon} is a square with one side called the
{em seam}. A {em closed ribbon} is a cylinder with one boundary
component called the {em seam}. We {em sew} an open (resp.~closed)
ribbon onto a graph by identifying the seam with an open (resp.~closed)
walk in the graph. A {em ribbon complex} is a graph with a finite number
of ribbons sewn on.
We investigate when a ribbon complex embeds in 3-dimensional Euclidean
space. We give several characterizations of such {em spatial} complexes
which lead to algorithms. We examine special cases where: 1) each edge
of the graph is incident with at most three ribbons, and 2) every ribbon is
closed together with a connectivity condition.

Topological Graph Theory, Embedding in 3-Space

Math Review Classification
Primary 05C10 ; Secondary 05C83

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21 Pages

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