An Improved Upper Bound for the Bilu-Linial Conjecture via Interlacing Families

Zhiqiang Xu, Xinyue Zhang

The Bilu-Linial conjecture asserts that every $d$-regular graph admits a signing $\sigma$ such that the spectral radius of the signed adjacency matrix $A_{\sigma }$ satisfies $ρ(A_σ)\le 2\sqrt{…