Author

Fredy Yip

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Preprint Oct 2026

Lower bounds for the magnitude of the minimum eigenvalue of graphs with applications to MaxCut and Chowla's cosine problem

Jin, Milojevi\'c, Tomon and Zhang established a powerful recursive estimate relating the positive eigenvalues of a graph whose least eigenvalue is small in absolute value. We establish a refinement of this result, yielding improved estimates across spectral graph theory and discrepancy theory, and for Chowla's cosine p...

Fredy Yip · 1 citation

Preprint Sep 2026

Tight bounds for positive discrepancy via eigenvalues

Given an $n\times n$ symmetric matrix $M$ with largest eigenvalue $\lambda_1\geq 0$, it is easy to show that the solution of the optimisation problem $\max_{v\in [-1,1]^n}v^TMv$ is at most $\lambda_1 n$. We prove the following converse: if every $n'\times n'$ principal submatrix of $M$ has maximal eigenvalue at least $...

Oliver Janzer, István Tomon, Fredy Yip · 1 citation