2604.01826 Empirical Density of Laman Graphs in the Critical Ensemble: Probability that a Random Graph with Exactly (2n-3) Edges is (2,3)-Sparse
Laman’s theorem states that a graph on n vertices is generically minimally rigid in the plane if and only if it has exactly 2n-3 edges and every induced subgraph on k >= 2 vertices satisfies the sparsity condition m' <= 2k-3. This paper presents a fully reproducible computational study of the empirical probability that a uniformly random graph with exactly m = 2n-3 edges is a true Laman graph.