Gary R. W. Greaves

collaborators

4 papers

math.CO2026

A proof of Haemers' toughness conjecture

Gary Greaves, Haoran Zhu

We prove that if $I^$ is a connected graph with minimum degree $I^´$ and Laplacian eigenvalues $0 = I^¼_{1} < I^¼_{2} ⩽ \dots ⩽ I^¼_{n}$ , then the toughness of $I^$ is bounded be…

math.PR2026

Spectral gap of biased adjacent-transposition chains

Gary R. W. Greaves, Haoran Zhu

We establish a sharp lower bound on the spectral gap of the biased adjacent-transposition Markov chain on the symmetric group. As a consequence, we resolve a longstanding conjectur…

math.CO2026

Aldous property for full-flag Johnson graphs

Gary Greaves, Haoran Zhu

We show that the full-flag Johnson graph has spectral gap equal to that of its Schreier quotient arising from the point-stabiliser equitable partition. Our results confirm two conj…

math.CO2025

Real-rooted integer polynomial enumeration algorithms and interlacing polynomials via linear programming

Gary R. W. Greaves, Jeven Syatriadi

We extend the algorithms of Robinson, Smyth, and McKee--Smyth to enumerate all real-rooted integer polynomials of a fixed degree, where the first few (at least three) leading coeff…