A random version of the Burr-Erd\H{o}s-Spencer theorem
Combinatorics
2026-05-22 v1
Abstract
A well-known result of Burr, Erd\H{o}s and Spencer [Transactions of the American Mathematical Society, 1975] determines the -colour Ramsey number for any sufficiently large collection of vertex-disjoint copies of a fixed graph without isolated vertices. In this short note we prove a random version of this result, thereby generalising the random Ramsey theorem of R\"odl and Ruci\'nski [Journal of the American Mathematical Society, 1995].
Cite
@article{arxiv.2605.22395,
title = {A random version of the Burr-Erd\H{o}s-Spencer theorem},
author = {Andrea Freschi and Ryan R. Martin and Andrew Treglown},
journal= {arXiv preprint arXiv:2605.22395},
year = {2026}
}
Comments
8 pages, 1 figure