English

Prague dimension of random graphs

Combinatorics 2023-12-20 v1 Discrete Mathematics Probability

Abstract

The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/log n for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n).

Cite

@article{arxiv.2011.09459,
  title  = {Prague dimension of random graphs},
  author = {He Guo and Kalen Patton and Lutz Warnke},
  journal= {arXiv preprint arXiv:2011.09459},
  year   = {2023}
}

Comments

20 pages

R2 v1 2026-06-23T20:21:12.372Z