Liana Yepremyan "Size-Ramsey numbers of powers of hypergraph trees and long subdivisions"
Liana Yepremyan from London School of Economics will give the talk "Size-Ramsey numbers of powers of hypergraph trees and long subdivisions" on the labs' Big Seminar.
Password: first 6 decimal places of $\pi$ after the decimal point
The $s$-colour size-Ramsey number of a hypergraph $H$ is the minimum number of edges in a hypergraph $G$ whose every $s$-edge-colouring contains a monochromatic copy of $H$.
We show that the $s$-colour size-Ramsey number of the $t$-power of the $r$-uniform tight path on $n$ vertices is linear in $n$, for every fixed $r, s, t$, thus answering a question of Dudek, La Fleur, Mubayi, and Rödl (2017).
In fact, we prove a stronger result that allows us to deduce that powers of bounded degree hypergraph trees and of `long subdivisions' of bounded degree hypergraphs have size-Ramsey numbers that are linear in the number of vertices. This extends recent results about the linearity of size-Ramsey numbers of powers of bounded degree trees and of long subdivisions of bounded degree graphs.
This is joint work with Shoham Letzter and Alexey Pokrovskiy.
Watch the video:
Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.