English

An O(n) time algorithm for finding Hamilton cycles with high probability

Data Structures and Algorithms 2020-12-07 v1 Combinatorics

Abstract

We design a randomized algorithm that finds a Hamilton cycle in O(n)\mathcal{O}(n) time with high probability in a random graph Gn,pG_{n,p} with edge probability pClogn/np\ge C \log n / n. This closes a gap left open in a seminal paper by Angluin and Valiant from 1979.

Keywords

Cite

@article{arxiv.2012.02551,
  title  = {An O(n) time algorithm for finding Hamilton cycles with high probability},
  author = {Rajko Nenadov and Angelika Steger and Pascal Su},
  journal= {arXiv preprint arXiv:2012.02551},
  year   = {2020}
}
R2 v1 2026-06-23T20:43:53.347Z