The largest hole in sparse random graphs

Nemanja Draganić; Stefan Glock; Michael Krivelevich

The largest hole in sparse random graphs

Combinatorics 2022-03-01 v2

Authors: Nemanja Draganić , Stefan Glock , Michael Krivelevich

Abstract

We show that for any $d=d(n)$ with $d_0(\epsilon) \le d =o(n)$ , with high probability, the size of a largest induced cycle in the random graph $G(n,d/n)$ is $(2\pm \epsilon)\frac{n}{d}\log d$ . This settles a long-standing open problem in random graph theory.

Cite

@article{arxiv.2106.00597,
  title  = {The largest hole in sparse random graphs},
  author = {Nemanja Draganić and Stefan Glock and Michael Krivelevich},
  journal= {arXiv preprint arXiv:2106.00597},
  year   = {2022}
}

Comments

to appear in RSA. arXiv admin note: substantial text overlap with arXiv:2102.09289

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