**Monday, October 26,** **3pm ET** (8pm BST, 8am Tue NZDT)

**Rose McCarty**, University of Waterloo

**Colouring pseudo-visibility graphs**

Youtube

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**Abstract:**

The *visibility graph* of a finite set of points $S$ on a Jordan curve $\mathcal{J}$ has vertex set $S$, and two points in $S$ are adjacent if the (open) segment between them is contained in the interior of $\mathcal{J}$. To obtain a *pseudo-visibility graph*, we instead start with a pseudolinear drawing of the complete graph with vertex set $S$ on $\mathcal{J}$. We show that any pseudo-visibility graph with clique number $\omega$ is $\left(3\cdot 4^{\omega-1}\right)$-colourable. This talk will also focus on connections between 1) developing efficient algorithms for recognizing these graphs and 2) constructing uniform, rank-$3$ oriented matroids which represent the pseudolinear drawing.

This is joint work with James Davies, Tomasz Krawczyk, and Bartosz Walczak.