Computing the number of realizations of a Laman graph

07/12/2017
by   Jose Capco, et al.
0

Laman graphs model planar frameworks which are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. In a recent paper we provide a recursion formula for this number of realizations using ideas from algebraic and tropical geometry. Here, we present a concise summary of this result focusing on the main ideas and the combinatorial point of view.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/19/2017

The number of realizations of a Laman graph

Laman graphs model planar frameworks that are rigid for a general choice...
research
01/03/2022

Realizations of Rigid Graphs

A minimally rigid graph, also called Laman graph, models a planar framew...
research
10/23/2017

Lower bounds on the number of realizations of rigid graphs

In this paper we take advantage of a recently published algorithm for co...
research
02/27/2022

Enumeration of chordal planar graphs and maps

We determine the number of labelled chordal planar graphs with n vertice...
research
06/16/2020

Confining the Robber on Cographs

In this paper, the notions of trapping and confining the robber on a gra...
research
08/04/2019

Computing the inverse geodesic length in planar graphs and graphs of bounded treewidth

The inverse geodesic length of a graph G is the sum of the inverse of th...
research
01/04/2018

Enumerating combinatorial triangulations of the hexahedron

Most indirect hexahedral meshing methods rely on 10 patterns of subdivis...

Please sign up or login with your details

Forgot password? Click here to reset