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arXiv · 2610.09972

A deterministic algorithm for signing bipartite graphs at the Ramanujan bound

Zhiqiang Xu
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Abstract

We give a deterministic polynomial-time algorithm for the Bilu--Linial signing problem on bipartite graphs. For every finite simple bipartite graph of maximum degree at most an integer $Δ\ge3$, the algorithm assigns signs to its edges so that the signed adjacency matrix has operator norm strictly less than $2\sqrt{Δ-1}$. Our algorithm builds on the randomized recursive repair framework of Jadbabaie, Saberi, and Sra~\cite{JSS26}, with deterministic rules for sign selection and vertex deletion.

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Zhiqiang Xu. 2026-10-07. A deterministic algorithm for signing bipartite graphs at the Ramanujan bound. https://arxiv.org/abs/2610.09972

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