Speaker
Lina Simbaqueba
(Universität Leipzig)
Description
Given a field $\mathbb{F}$ and a directed graph $G$ with vertex set $\{1, 2, \ldots, n\}$, we define the minrank $\text{mr}_F(G)$ to be the minimum rank over all matrices $M$ with nonzero diagonal such that $M(i,j) = 0$ whenever $ij$ is not a directed edge. In this talk, we will discuss the problem of minimizing $\text{mr}_F(G)$ over all tournaments on $n$ vertices, as well as the problem of determining the typical value of $\text{mr}_F(T)$ for a random tournament $T$ on $n$ vertices.
Author
Dr
Igor Balla
(Universität Leipzig)
Co-authors
Dr
Leo Versteegen
(London School of Economics and Poltical Science)
Lina Simbaqueba
(Universität Leipzig)