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math.CO2025
Remarks on the Brouwer Conjecture
Oliver Knill
The Brouwer conjecture (BC) in spectral graph theory claims that the sum of the largest k Kirchhoff eigenvalues of a graph are bounded above by the number m of edges plus k(k+1)/2.…
math.CO2025
Soft Barycentric Refinement
Oliver Knill
The soft Barycentric refinement preserves manifolds with or without boundary. In every dimension larger than one, there is a universal spectral central limiting measure that has af…
math.CO2024
Morse and Lusternik-Schnirelmann for graphs
Oliver Knill
Both Morse theory and Lusternik-Schnirelmann theory link algebra, topology and analysis in a geometric setting. The two theories can be formulated in finite geometries like graph t…