Rigid two-dimensional frameworks with three collinear points

Bill Jackson, Tibor Jordan

Research output: Contribution to journalReview article

2 Citations (Scopus)


Let G = (V, E) be a graph and x, y, z ∈ V be three designated vertices. We give a necessary and sufficient condition for the existence of a rigid two-dimensional framework (G, p), in which x, y, z are collinear. This result extends a classical result of Laman on the existence of a rigid framework on G. Our proof leads to an efficient algorithm which can test whether G satisfies the condition.

Original languageEnglish
Pages (from-to)427-444
Number of pages18
JournalGraphs and Combinatorics
Issue number4
Publication statusPublished - Dec 1 2005


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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