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The Grone Merris Conjecture and a quadratic eigenvalue problem

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arxiv math/0512647 v1 pith:PBCNIIFV submitted 2005-12-29 math.CA math.CO

Nets Hawk Katz This is my paper · ORCID
classification math.CAmath.CO
keywords conjecturegronemerriscalculusclasscurveeigenvaluefirst
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We verify the Grone Merris conjecture for a class of graphs. We do this by curve sketching in the sense of first year calculus. That is, we do it by homotopy methods.

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Cited by 2 Pith papers

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  1. The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality

    math.CO 2026-07 accept novelty 8.0 of 10

    The Duval–Reiner majorization conjecture fails for every r≥5, while the r=2 inequality holds universally with an explicit equality classification.

  2. Sums of Laplacian eigenvalues and sums of degrees

    math.CO 2025-08 conditional novelty 7.0 of 10

    For any simplicial complex, the sum of the k largest upper-Laplacian eigenvalues is at most the sum of the (r+1)k largest r-degrees of (r-1)-faces, with applications to graphs and partite complexes.

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