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Flexible circuits in the d‐dimensional rigidity matroid

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dc.contributor.authorGrasegger, Georg
dc.contributor.authorGuler, Hakan
dc.contributor.authorJackson, Bill
dc.contributor.authorNixon, Anthony
dc.date.accessioned2026-01-04T16:01:10Z
dc.date.issued2021-12-06
dc.description.abstractAbstractA bar‐joint framework in is rigid if the only edge‐length preserving continuous motions of the vertices arise from isometries of . It is known that, when is generic, its rigidity depends only on the underlying graph , and is determined by the rank of the edge set of in the generic ‐dimensional rigidity matroid . Complete combinatorial descriptions of the rank function of this matroid are known when , and imply that all circuits in are generically rigid in when . Determining the rank function of is a long standing open problem when , and the existence of nonrigid circuits in for is a major contributing factor to why this problem is so difficult. We begin a study of nonrigid circuits by characterising the nonrigid circuits in which have at most vertices.
dc.description.urihttps://doi.org/10.1002/jgt.22780
dc.description.urihttp://arxiv.org/pdf/2003.06648
dc.description.urihttps://dx.doi.org/10.48550/arxiv.2003.06648
dc.description.urihttp://arxiv.org/abs/2003.06648
dc.description.urihttps://zbmath.org/7746074
dc.description.urihttps://eprints.lancs.ac.uk/id/eprint/162304/
dc.description.urihttps://doi.org/https://doi.org/10.1002/jgt.22780
dc.identifier.doi10.1002/jgt.22780
dc.identifier.eissn1097-0118
dc.identifier.endpage330
dc.identifier.issn0364-9024
dc.identifier.openairedoi_dedup___::a578afb5539ebc6fe2f3ce669229a6c4
dc.identifier.orcid0000-0001-7421-8115
dc.identifier.orcid0000-0003-3300-860x
dc.identifier.orcid0000-0003-0639-1295
dc.identifier.scopus2-s2.0-85143914109
dc.identifier.startpage315
dc.identifier.urihttps://hdl.handle.net/20.500.12597/39217
dc.identifier.volume100
dc.identifier.wos000726755600001
dc.language.isoeng
dc.publisherWiley
dc.relation.ispartofJournal of Graph Theory
dc.rightsOPEN
dc.subjectrigidity matroid
dc.subjectMetric Geometry (math.MG)
dc.subjectCombinatorial aspects of matroids and geometric lattices
dc.subjectrigid graph
dc.subjectC25, 05C10
dc.subjectPlanar graphs
dc.subjectgeometric and topological aspects of graph theory
dc.subjectMathematics - Metric Geometry
dc.subjectRigidity and flexibility of structures (aspects of discrete geometry)
dc.subjectFOS: Mathematics
dc.subjectbar-joint framework
dc.subjectMathematics - Combinatorics
dc.subjectCombinatorics (math.CO)
dc.subjectflexible circuit
dc.titleFlexible circuits in the d‐dimensional rigidity matroid
dc.typeArticle
dspace.entity.typePublication
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