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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Constructing isostatic frameworks for the ℓ1and ℓ∞-plane
AU - Clinch, Katie
AU - Kitson, Derek
PY - 2020/6/12
Y1 - 2020/6/12
N2 - We 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)=(p1(v),p2(v)), such that |pi(u)−pi(v)|⩾|p3−i(u)−p3−i(v)| 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 ℓ1 or ℓ∞-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.
AB - We 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)=(p1(v),p2(v)), such that |pi(u)−pi(v)|⩾|p3−i(u)−p3−i(v)| 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 ℓ1 or ℓ∞-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.
U2 - 10.37236/8196
DO - 10.37236/8196
M3 - Journal article
VL - 27
JO - The Electronic Journal of Combinatorics
JF - The Electronic Journal of Combinatorics
SN - 1077-8926
IS - 2
M1 - P2.49
ER -