5 papers
-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…
The number of realisations of a random graph
Sean Dewar, Anthony Nixon, Ben Smith
Determining the number of realisations of a graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we prove that the -dimensi…
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…
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…
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…