# Hurtado, Ferran

## Chromatic number of associahedron ★★

Author(s): Fabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood

**Conjecture**Associahedra have unbounded chromatic number.

## Edge-Colouring Geometric Complete Graphs ★★

Author(s): Hurtado

**Question**What is the minimum number of colours such that every complete geometric graph on vertices has an edge colouring such that:

- \item[Variant A] crossing edges get distinct colours, \item[Variant B] disjoint edges get distinct colours, \item[Variant C] non-disjoint edges get distinct colours, \item[Variant D] non-crossing edges get distinct colours.

Keywords: geometric complete graph, colouring

## 3-Colourability of Arrangements of Great Circles ★★

Author(s): Felsner; Hurtado; Noy; Streinu

Consider a set of great circles on a sphere with no three circles meeting at a point. The arrangement graph of has a vertex for each intersection point, and an edge for each arc directly connecting two intersection points. So this arrangement graph is 4-regular and planar.

**Conjecture**Every arrangement graph of a set of great circles is -colourable.

Keywords: arrangement graph; graph coloring