May 18 – 22, 2026
Virginia Tech
America/New_York timezone

On the minrank of a tournament

May 21, 2026, 11:50 AM
25m
Goodwin Hall 155

Goodwin Hall 155

Contributed Talk Contributed Talks Contributed Talks

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)

Presentation materials

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