Georgia Institute of Technology College of Sciences

Various notions of dimension are important throughout mathematics, and for graphs the so-called Prague dimension 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 $O(\log n)$.

Based on joint work with He Guo and Lutz Warnke.