Year: 2026
Type: preprint
Abstract: We prove that, for every $\eps>0$, any $n$-vertex graph that needs at least $\eps n^2$ edge changes to become a Turán graph has positive discrepancy at least $c_\eps n^{5/4}$. Consequently, every such regular graph has second eigenvalue at least $c'_\eps n^{1/4}$. These results prove two conjectures of Räty, Sudakov and Tomon.
Source: arXiv (Cornell University)
Authors: Xu, Leyou, Zhou, Bo
Institution: South China Normal University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220748488