Bound Ramsey-type graph parameters using spectral eigenvalue bounds.
npx skills add https://github.com/bneb/perqed --skill spectral-graph-bounds
Please help me install this Agent Skill. Skill: spectral_graph_bounds Source: https://github.com/bneb/perqed/tree/main/.agents/skills/spectral_graph_bounds Command: npx skills add https://github.com/bneb/perqed --skill spectral-graph-bounds
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.
Run a spectral SA pass to minimize the gap between the largest and smallest eigenvalues as a proxy for Ramsey-bound guidance.
High-intent search queries and answers about installing and using this skill.
Bound Ramsey numbers by translating discrete subgraph existence into the continuous eigenvalue spectrum of an adjacency matrix, applying Hoffman and Lovász theta bounds to constrain clique and independent set sizes without exhaustive search.
The Hoffman bound uses the minimum eigenvalue of the adjacency matrix to set a tight upper limit on the independence number alpha(G), while Lovász theta provides complementary SDP-based bounds to constrain omega(G) without enumerating subgraphs.
Yes, simulated annealing leverages energy-based reformulations driven by smooth eigenvalue gradients to navigate graph configurations, minimizing the gap between the largest and smallest eigenvalues as a proxy for Ramsey-bound guidance.
Apply the Expander Mixing Lemma alongside spectral bounds to guide combinatorial searches in large expander graphs, using eigenvalue distributions to constrain subgraph existence and inform energy formulations during optimization.
Working with these spectral bounds requires understanding semidefinite programming, Lovász theta, and Hoffman bound mechanics, as these formulate the energy functions and gradient-based optimization used to constrain Ramsey-type parameters.
Avoid spectral bounds when exact subgraph counts are required rather than theoretical limits, or when adjacency matrix eigenvalue computations become intractable for extremely dense graph instances.
plurigridCompute the Ihara zeta function for graphs using the Bass-Hashimoto determinant formula.
kishorkukrejaSolve the Traveling Salesman Problem with exact, heuristic, and metaheuristic algorithms.
NVIDIAModel quadratic programming problems with objectives, variables, and linear constraints for cuOpt.
scooter-lacroixSolve optimization problems with gradient descent, momentum, and Newton's methods.
