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The Petersen graph has 10 vertices and 15 edges, and every vertex has degree 3. Its adjacency matrix is easy to write down, and its eigenvalues are 3, then 1 with multiplicity 5, then −2 with multiplicity 4. The Hoffman bound then gives an independence number of at most 4, which is attained.
The same argument applies to the wider family, and we conjecture that the bound is attained for every Kneser graph K(n, 2).
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We prove the solver terminates on every input, and on the 14 benchmark instances it matches the best known values. If the noise is Gaussian, the error falls as 1/√n, and we expect the same rate for heavy-tailed noise.
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