论文标题
刚性图的实现
Realizations of Rigid Graphs
论文作者
论文摘要
一个最小的刚性图，也称为Laman图，建模了一个平面框架，该框架是其顶点之间一般距离的一般选择。换句话说，在平面上实现这样的图形有限多种方式，直到同轴形成。使用代数和热带几何形状的思想，我们得出了此类实现数量的递归公式。将计算结果与通过胶合技术构建新的刚性图的结合，我们可以在具有给定数量的顶点的图形的最大实现数量上给出新的下限。
A minimally rigid graph, also called Laman graph, models a planar framework which is rigid for a general choice of distances between its vertices. In other words, there are finitely many ways, up to isometries, to realize such a graph in the plane. Using ideas from algebraic and tropical geometry, we derive a recursive formula for the number of such realizations. Combining computational results with the construction of new rigid graphs via gluing techniques, we can give a new lower bound on the maximal possible number of realizations for graphs with a given number of vertices.
