Frameworks with coordinated edge motions

Bernd Schulze, Hattie Serocold, Louis Simon Theran

Research output: Contribution to journalArticlepeer-review


We develop a rigidity theory for bar-joint frameworks in Euclidean d-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class. Rigidity for these coordinated frameworks is a generic property, and we characterize the rigid graphs in terms of redundant rigidity in the standard d-dimensional rigidity matroid. We also interpret our main results in terms of matroid unions.
Original languageEnglish
Pages (from-to)2602-2618
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Issue number4
Publication statusPublished - 9 Nov 2022


  • Coordinated constraint relaxation
  • Bar-joint frameworks
  • Rigidity
  • Infinitesimal rigidity
  • Rigidity matroid


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