On October 31, 2023, James Davies from the University of Cambridge gave a talk at the Discrete Math Seminar on the coloring of the plane so that two points odd distance apart have distinct colors. The title of his talk was “Odd distances in colourings of the plane“.
We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd integral distance from each other.
On April 11, 2023, James Davies from the University of Cambridge gave a talk at the Discrete Math Seminar on his two theorems stating that proper pivot-minor-closed classes of graphs are 𝜒-bounded and have the strong Erdős-Hajnal property. The title of his talk is “two structural results for pivot-minors.”
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.
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“.