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Rigid frameworks with dilation constraints

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Rigid frameworks with dilation constraints. / Dewar, Sean; Nixon, Anthony; Sainsbury, Andrew.
In: Discrete Mathematics, Vol. 348, No. 2, 114304, 28.02.2025.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dewar, S, Nixon, A & Sainsbury, A 2025, 'Rigid frameworks with dilation constraints', Discrete Mathematics, vol. 348, no. 2, 114304. https://doi.org/10.1016/j.disc.2024.114304

APA

Dewar, S., Nixon, A., & Sainsbury, A. (2025). Rigid frameworks with dilation constraints. Discrete Mathematics, 348(2), Article 114304. https://doi.org/10.1016/j.disc.2024.114304

Vancouver

Dewar S, Nixon A, Sainsbury A. Rigid frameworks with dilation constraints. Discrete Mathematics. 2025 Feb 28;348(2):114304. Epub 2024 Oct 31. doi: 10.1016/j.disc.2024.114304

Author

Dewar, Sean ; Nixon, Anthony ; Sainsbury, Andrew. / Rigid frameworks with dilation constraints. In: Discrete Mathematics. 2025 ; Vol. 348, No. 2.

Bibtex

@article{b65fde4ae3454cee9a474d42879ca6e0,
title = "Rigid frameworks with dilation constraints",
abstract = "We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean d-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints.",
keywords = "Rigid graph, Bar-joint framework, Generic rigidity, Global rigidity, Dilation constraints",
author = "Sean Dewar and Anthony Nixon and Andrew Sainsbury",
year = "2025",
month = feb,
day = "28",
doi = "10.1016/j.disc.2024.114304",
language = "English",
volume = "348",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Rigid frameworks with dilation constraints

AU - Dewar, Sean

AU - Nixon, Anthony

AU - Sainsbury, Andrew

PY - 2025/2/28

Y1 - 2025/2/28

N2 - We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean d-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints.

AB - We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean d-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then consider generic global rigidity. In particular, we provide an algebraic sufficient condition and a weak necessary condition. We also construct a large family of globally rigid frameworks and conjecture a combinatorial characterisation when most coordinate directions have dilation constraints.

KW - Rigid graph

KW - Bar-joint framework

KW - Generic rigidity

KW - Global rigidity

KW - Dilation constraints

U2 - 10.1016/j.disc.2024.114304

DO - 10.1016/j.disc.2024.114304

M3 - Journal article

VL - 348

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2

M1 - 114304

ER -