Alan Lew

activity

20242026

collaborators

6 papers

math.CO2026

Rigidity of expanders and pseudorandom graphs

Michael Krivelevich, Alan Lew, Peleg Michaeli

A graph $G = (V, E)$ is called $d$ -rigid if, for a generic embedding of its vertices in $R^{d}$ , the only continuous motions of the vertices preserving the distances between al…

math.CO2026

Combinatorial sufficient conditions for graph rigidity and applications to random graphs

Michael Krivelevich, Alan Lew, Peleg Michaeli

A graph $G = (V, E)$ is called $d$ -rigid if, for a generic embedding of its vertices in $R^{d}$ , every edge-length preserving continuous motion of the vertices preserves the di…

math.CO2025

Stiffness matrices of graph blow-ups and the $d$ -dimensional algebraic connectivity of complete bipartite graphs

Yunseong Jung, Alan Lew

The $d$ -dimensional algebraic connectivity $a_{d} (G)$ of a graph $G = (V, E)$ is a quantitative measure of its $d$ -dimensional rigidity, defined in terms of the eigenvalues of stiffness…

math.CO2025

On the $k$ -volume rigidity of a simplicial complex in $R^{d}$

Alan Lew, Eran Nevo, Yuval Peled +1

We define a generic rigidity matroid for $k$ -volumes of a simplicial complex in $R^{d}$ , and prove that for $2 \leq k \leq d - 1$ it has the same rank as the classical generic…

math.CO2024

Minimum degree conditions for graph rigidity

Michael Krivelevich, Alan Lew, Peleg Michaeli

We study minimum degree conditions that guarantee that an $n$ -vertex graph is rigid in $R^{d}$ . For small values of $d$ , we obtain a tight bound: for $d = O (n)$ , ever…

math.CO2024

Laplacian eigenvalues of independence complexes via additive compound matrices

Alan Lew

The independence complex of a graph $G = (V, E)$ is the simplicial complex $I (G)$ on vertex set $V$ whose simplices are the independent sets in $G$ . We present new lower bounds on the…

Rigidity of expanders and pseudorandom graphs

Combinatorial sufficient conditions for graph rigidity and applications to random graphs

Stiffness matrices of graph blow-ups and the d-dimensional algebraic connectivity of complete bipartite graphs

On the k-volume rigidity of a simplicial complex in Rd

Minimum degree conditions for graph rigidity

Laplacian eigenvalues of independence complexes via additive compound matrices

Stiffness matrices of graph blow-ups and the $d$ -dimensional algebraic connectivity of complete bipartite graphs

On the $k$ -volume rigidity of a simplicial complex in $R^{d}$