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. <p> 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. |
Keywords
Topological Graph Theory, Embedding in 3-Space
Math Review Classification
Primary 05C10
; Secondary 05C83
Last Updated
Length
21 Pages
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