Graph Theory and Combinatorics Seminar

Speaker: József Balogh (UIUC)

Title: Even smaller universal posets

Abstract: Bastide, Groenland and Nenadov showed that there is a poset $P$ of size $ 2^{\left(1+o(1)\right)2n/3}$, which is universal  for the family of $n$-element posets. We improve upon their result, by providing such universal poset of size $2^{(1+o(1))n/2}$. This result is a step towards the conjectured minimum size $2^{(1+o(1))n/4}$.

It is joint work with Ramon I. Garcia and Marcelo Sales.