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dc.contributor.creatorClinch, Katie
dc.contributor.creatorKitson, Derek
dc.date.accessioned2021-03-25T14:47:38Z
dc.date.available2021-03-25T14:47:38Z
dc.date.issued2020-06-12
dc.identifier.citationKitson, D. & Clinch, K. (2020) 'Constructing isostatic frameworks for the l1 and l infinity plane', Electronic Journal of Combinatorics, 27(2), available: https://doi.org/10.37236/8196.en_US
dc.identifier.urihttps://dspace.mic.ul.ie/handle/10395/2964
dc.description.abstractWe use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G = (V,E) has a partition into two spanning trees T1 and T2 then there is a map p : V → R2, p(v) = (p(v)1,p(v)2), such that |p(u)i −p(v)i| > |p(u)3−i−p(v)3−i| for every edge uv in Ti (i = 1,2). As a consequence, we solve an open problem on the realisability of minimally rigid bar-joint frameworks in the `1 or `∞-plane. We also show how to adapt this technique to incorporate symmetry and indicate several related open problems on rigidity, redundant rigidity and forced symmetric rigidity in normed spaces.en_US
dc.language.isoengen_US
dc.publisherElectronic Journal of Combinatoricsen_US
dc.relation.ispartofseries27;2
dc.rightsOpen Accessen_US
dc.rights.urihttps://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i2p49en_US
dc.subjectBar-joint frameworken_US
dc.subjectInfinitesimal rigidityen_US
dc.subjectManhattan metricen_US
dc.subjectSpanning tree decompositionen_US
dc.subjectSparse multigraphen_US
dc.titleConstructing isostatic frameworks for the l1 and l infinity plane (Pre-published)en_US
dc.typeArticleen_US
dc.type.supercollectionall_mic_researchen_US
dc.type.supercollectionmic_published_revieweden_US
dc.description.versionYesen_US
dc.identifier.doi10.37236/8196


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