English

Random graph's Hamiltonicity is strongly tied to its minimum degree

Combinatorics 2019-12-20 v2

Abstract

We show that the probability that a random graph GG(n,p)G\sim G(n,p) contains no Hamilton cycle is (1+o(1))Pr(δ(G)<2)(1+o(1))Pr(\delta (G) < 2) for all values of p=p(n)p = p(n). We also prove an analogous result for perfect matchings.

Keywords

Cite

@article{arxiv.1810.04987,
  title  = {Random graph's Hamiltonicity is strongly tied to its minimum degree},
  author = {Yahav Alon and Michael Krivelevich},
  journal= {arXiv preprint arXiv:1810.04987},
  year   = {2019}
}
R2 v1 2026-06-23T04:36:13.699Z