University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Rigidity of graphs

Rigidity of graphs

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  • UserAnthony Nixon, Lancaster
  • ClockThursday 13 October 2022, 15:00-16:00
  • HouseLTC.

If you have a question about this talk, please contact Johannes Carmesin.

A (bar-joint) framework is the combination of a graph G and a map p assigning positions in Euclidean d-space to the vertices of G. The vertices are modelled as universal joints and the edges as stiff bars. The framework is rigid if the only edge-length-preserving continuous deformation of the vertices arises from an isometry of the space. While it is computationally difficult to determine if a given framework is rigid, the generic behaviour depends only on the graph. Indeed, when d=1, G is rigid if and only if it is connected, and when d=2, a precise combinatorial description was obtained by Polaczek-Geiringer in the 1920s. However, giving a combinatorial description in all higher dimensions remains open 100 years later. The talk will survey graph rigidity and then report on recent joint work on a particular special case as well as an application to maximum likelihood estimation.

This talk is part of the Combinatorics and Probability seminar series.

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