spectral_graph_bounds

What problem does it solve?

Translate discrete subgraph existence (counting cliques and independent sets) into the continuous eigenvalue spectrum of the adjacency matrix, leveraging smooth spectral gradients and Hoffman/Lovász theta bounds to set tight limits on Ramsey numbers and guide SA energy reformulations.

Core Features & Use Cases

• Spectral bounds to constrain alpha(G) and omega(G) without exhaustive subgraph search, using Hoffman bound and Lovász theta.
• Energy-based reformulations for simulated annealing that leverage eigenvalue gradients to navigate graph configurations.
• Applicable to graph construction, Ramsey-type bounding problems, and expander-based reasoning in large graphs.

Quick Start

Run a spectral SA pass to minimize the gap between the largest and smallest eigenvalues as a proxy for Ramsey-bound guidance.