4 citations · 4 across the 7 of their papers we have counts for
3 papers · 1 filter
The phylogenetic rank of a graph
Franklin Ashworth, Oliver Clarke, Jeffrey Giansiracusa +3
The Pachter-Sturmfels phylogenetic rank of a graph G is the minimal number of metric trees needed to embed G isometrically. Here, all edges of G are of length one and the product o…
The tropical galaxy of a Laman graph
Amelia Bielby, Arushi Chauhan, Cassia Pearce +1
A Laman graph is a minimally rigid graph in dimension two, and its realization number is its number of distinct embeddings with fixed generic edge lengths. While conjectured to…
A tropical approach to rigidity: counting realisations of frameworks
Oliver Clarke, Sean Dewar, Daniel Green Tripp +4
A realisation of a graph in the plane as a bar-joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these f…