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Coincident Rigidity of 2-Dimensional Frameworks

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Abstract

Fekete, Jordán and Kaszanitzky (Graphs Combin 31:585–599, 2015) characterised the graphs which can be realised as 2-dimensional, infinitesimally rigid, bar-joint frameworks in which two given vertices are coincident. We formulate a conjecture which would extend their characterisation to an arbitrary set T of vertices and verify our conjecture when \(|T|=3\).

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Acknowledgements

We would like to thank Shin-ichi Tanigawa for a helpful converstaion which gave rise to the \(K_{5,5}\) example in Sect. 5.2.

Funding

The first author would also like to thank the Ministry of National Education of Turkey for PhD funding through a YLSY grant.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Kastamonu University, Kastamonu, Turkey

    Hakan Guler

  2. School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Bill Jackson

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  1. Hakan Guler
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  2. Bill Jackson
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Correspondence to Hakan Guler.

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Guler, H., Jackson, B. Coincident Rigidity of 2-Dimensional Frameworks. Graphs and Combinatorics 38, 128 (2022). https://doi.org/10.1007/s00373-022-02540-9

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