Generalizes Brouwer's conjecture on Laplacian spectra to simplicial complexes and proves it for shifted complexes, simplicial trees, first/second/last partial sums for all complexes, and additional cases based on dimension and matching number.
The Grone-Merris conjecture
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A Conjectural Brouwer Inequality for Higher-Dimensional Laplacian Spectra
Generalizes Brouwer's conjecture on Laplacian spectra to simplicial complexes and proves it for shifted complexes, simplicial trees, first/second/last partial sums for all complexes, and additional cases based on dimension and matching number.