Sewing ribbons on graphs in space

  • Authors:

  • Dan Archdeacon;C. Paul Bonnington;R. Bruce Richter;Jozef Sirán

  • Affiliations:

  • Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont;Department of Mathematics, University of Auckland, Auckland, New Zealand;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada;Department of Mathematics, SvF, Slovak University of Technology, 813 68 Bratislava, Slovakia

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2002

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Abstract

An open ribbon is a square with one side called the seam. A closed ribbon is a cylinder with one boundary component called the seam. We sew an open (resp. closed) ribbon onto a graph by identifying the seam with an open (resp. closed) walk in the graph. A 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 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.