PIMS-UVic Discrete Math Seminar: Liana Yepremyan

  • Date: 03/11/2021
  • Time: 10:00
Lecturer(s):
Liana Yepremyan, University of Illinois Chicago and London School of Economics
Location: 

Online

Topic: 

Size-Ramsey numbers of powers of hypergraph trees and long subdivisions [video]

Description: 

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 R\"odl (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.

Other Information: 

This event took place via zoom. A recording is available on mathtube.org.