Pivot-minors can be thought of as a dense analogue of graph minors. We shall discuss pivot-minors and two recent results for proper pivot-minor-closed classes of graphs. In particular, that for every graph H, the class of graphs containing no H-pivot-minor is 𝜒-bounded, and also satisfies the (strong) Erdős-Hajnal property.
James Davies gave an online talk disproving Esperet’s conjecture on the polynomial 𝜒-boundedness of graph classes at the Virtual Discrete Math Colloquium
On February 10, 2022, James Davies from University of Waterloo gave an online talk at the Virtual Discrete Math Colloquium disproving Esperet’s conjecture on the polynomial 𝜒-boundedness of graph classes. The title of his talk was “Separating polynomial 𝜒-boundedness from 𝜒-boundedness“.