Event Details

Speaker: Rebecca Monks (Lancaster)

Title: 5-regular graphs and the 3-dimensional rigidity matroid

Abstract: A bar-joint framework (G,p) in Euclidean d-space is rigid if the only edge-length-preserving continuous motions arise from isometries of R^d. In the generic case, rigidity is determined by the generic d-dimensional rigidity matroid of G. The combinatorial nature of this matroid is well understood when d=1,2 but open when d>2. Jackson and Jordán characterised independence in the generic d-dimensional rigidity matroid for connected graphs with minimum degree at most d+1 and maximum degree at most d+2. The next step would be to prove a similar characterisation for (d+2)-regular graphs, which is known to be false when d>3, leaving open the case when d=3. In this talk I will present joint work with Tony Nixon, introducing our result resolving the open case and explaining some of the key steps in the proof.