## James Davies gave a talk on the coloring of the plane so that points odd distance apart get distinct colors at the Discrete Math Seminar

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“.

## James Davies, 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.

## James Davies gave a talk on the 𝜒-boundedness and the strong Erdős-Hajnal property of proper pivot-minor-closed classes of graphs at the Discrete Math Seminar

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.”

## James Davies, 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.

## 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“.

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