6 papers · 1 filter
Rigidity of complements of bounded-degree graphs
John Haslegrave, Peleg Michaeli, Anthony Nixon
Maxwell observed that the graph of any rigid generic framework in on vertices has at least edges. In this article we prove that graphs whose…
On Generic Linearly Constrained Frameworks
Zakir Deniz, Hakan Guler, Anthony Nixon
A linearly constrained framework in is a bar-joint framework where, in addition, vertices with loops are constrained to lie in given affine subspaces. In the generic…
The number of realisations of a random graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of realisations, up to isometries, of a graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we prove t…
Sharp thresholds for NAC-colourings and stable cuts in random graphs
Katie Clinch, John Haslegrave, Tony Huynh +1
NAC-colourings of graphs correspond to flexible quasi-injective realisations in . A special class of NAC-colourings are those that arise from stable cuts. We give s…
-fold circuits and coning in rigidity matroids
John Hewetson, Bill Jackson, Anthony Nixon +1
In 1980 Lovász introduced the concept of a double circuit in a matroid. The 2nd, 3rd and 4th authors recently generalised this notion to -fold circuits (for any natural number $…
5-regular graphs and the 3-dimensional rigidity matroid
Rebecca Monks, Anthony Nixon
A bar-joint framework in Euclidean -space is rigid if the only edge-length-preserving continuous motions arise from isometries of . In the generic case, ri…