Rigid Two-Dimensional Frameworks with Two Coincident Points

Zsolt Fekete, Tibor Jordán, Viktória E. Kaszanitzky

Research output: Contribution to journalArticle

3 Citations (Scopus)


Let G = (V, E) be a graph and u,v∈V be two distinct vertices. We give a necessary and sufficient condition for the existence of an infinitesimally rigid two-dimensional bar-and-joint framework (G, p), in which the positions of u and v coincide. We also determine the rank function of the corresponding modified generic rigidity matroid on ground-set E. The results lead to efficient algorithms for testing whether a graph has such a coincident realization with respect to a designated vertex pair and, more generally, for computing the rank of G in the matroid.

Original languageEnglish
Pages (from-to)585-599
Number of pages15
JournalGraphs and Combinatorics
Issue number3
Publication statusPublished - May 1 2015


  • Bar-and-joint framework
  • Infinitesimal rigidity
  • Rigid graph
  • Rigidity matroid

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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