Year: 2026
Type: preprint
Abstract: We show that, for some absolute constants $c_1,c_2>0$, every $(n,d,λ)$-graph with $λ\le c_1 d$ contains an induced cycle of length at least $c_2n\log(d/λ)/d$. This is best possible up to the values of $c_1,c_2$. Our techniques include a multi-scale algorithmic analysis, an adapted depth-first exploration procedure, a link to percolation theory, and estimates for random row-and-column extraction in symmetric matrices.
Source: arXiv (Cornell University)
Institutions: ETH Zurich, TU Wien, Tel Aviv University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7211992231