# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, June 26, 2018, 12:15 pm

**Duration**: 30 minutes

**Location**: CHN C 14

**Speaker**: Pavel Valtr (Charles University)

## The exact chromatic number of the convex segment disjointness graph

Let P be a set of n points in strictly convex position in the plane. Let D_n be the graph whose vertex set is the set of all line segments with endpoints in P, where disjoint segments are adjacent. The chromatic number of this graph was first studied by Araujo, Dumitrescu, Hurtado, Noy, and Urrutia [2005] and then by Dujmovic and Wood [2007]. Improving on their estimates, we prove the following exact formula for the chromatic graph of D_n: \chi(D_n)=n-[\sqrt{n+1/4}-1/2]. Joint work with Ruy Fabila-Monroy, Jakob Jonsson, and David Wood.

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