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A necessary condition for generic rigidity of bar‐and‐joint frameworks in d‐space

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dc.contributor.authorGuler, Hakan
dc.contributor.authorJackson, Bill
dc.date.accessioned2026-01-04T15:44:33Z
dc.date.issued2021-09-08
dc.description.abstractAbstractA graph is ‐sparse if each subset with induces at most edges in . Maxwell showed in 1864 that a necessary condition for a generic bar‐and‐joint framework with at least vertices to be rigid in is that should have a ‐sparse subgraph with edges. This necessary condition is also sufficient when but not when . Cheng and Sitharam strengthened Maxwell's condition by showing thateverymaximal ‐sparse subgraph of should have edges when . We extend their result to all .
dc.description.urihttps://doi.org/10.1002/jgt.22737
dc.description.urihttp://arxiv.org/pdf/1104.4415
dc.description.urihttps://dx.doi.org/10.48550/arxiv.1104.4415
dc.description.urihttp://arxiv.org/abs/1104.4415
dc.description.urihttps://zbmath.org/7745265
dc.description.urihttps://dx.doi.org/10.1002/jgt.22737
dc.identifier.doi10.1002/jgt.22737
dc.identifier.eissn1097-0118
dc.identifier.endpage239
dc.identifier.issn0364-9024
dc.identifier.openairedoi_dedup___::f2e911f98c8b318686aa4f11e181de03
dc.identifier.orcid0000-0003-3300-860x
dc.identifier.scopus2-s2.0-85114369671
dc.identifier.startpage231
dc.identifier.urihttps://hdl.handle.net/20.500.12597/39033
dc.identifier.volume99
dc.identifier.wos000693646600001
dc.language.isoeng
dc.publisherWiley
dc.relation.ispartofJournal of Graph Theory
dc.rightsOPEN
dc.subjectrigidity matroid
dc.subjectGraph representations (geometric and intersection representations, etc.)
dc.subjectC25, 05C62, 70B15
dc.subjectCombinatorial aspects of matroids and geometric lattices
dc.subjectPlanar graphs
dc.subjectgeometric and topological aspects of graph theory
dc.subjectinfinitesimal rigidity
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.titleA necessary condition for generic rigidity of bar‐and‐joint frameworks in d‐space
dc.typeArticle
dspace.entity.typePublication
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