English

On rainbow thresholds

Combinatorics 2024-08-13 v2 Probability

Abstract

Resolving a recent problem of Bell, Frieze, and Marbach, we establish both the threshold result of Frankston--Kahn--Narayanan--Park, and its strengthening by Spiro, in the rainbow setting. This has applications to the thresholds for rainbow structures in random graphs where each edge is given a uniformly random color from a set of given colors.

Cite

@article{arxiv.2310.03974,
  title  = {On rainbow thresholds},
  author = {Jie Han and Xiaofan Yuan},
  journal= {arXiv preprint arXiv:2310.03974},
  year   = {2024}
}

Comments

11 pages + appendix. New results added! We extend Spiro-spread to the rainbow setting as well, which in particular implies the rainbow thresholds for power of Hamilton cycles and hypergraph Hamilton ell-cycles

R2 v1 2026-06-28T12:42:12.477Z