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