Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, November 28, 2019, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Pascal Su

The Erdős-Rényi random graph model was first introduced by Erdős and Rényi in the late 1950's and is still of great interest in the field of combinatorics. In particular we are interested in the chromatic number of a random graph. Bollobás proved the chromatic number is asymptotically \chi(G_{n,1/2}) ~ n/( 2 log_{2} n ), for general constants p in (0,1) we now know \chi(G_{n,p}) ~ (log_{2} (1/(1-p)) n )/(2 log_{2} n) and there also exists work on lower order terms. The G_{n,p} model has many useful properties, but in some instances it might be too homogeneous and not flexible enough. We want to look at the random block graph model which can be viewed as a finer partition of the G_{n,p} random graph model. A quick description is partition the vertex set into a constant amount of sets, all of linear size, and place a random graph on every set and random bipartite graphs between every pair of sets and each of the probabilities p can vary. The chromatic number of this graph can be bounded, with a coupling, from above and below with \chi(G_{n, p_{min}}) and \chi(G_{n, p_{max}}) respectively. We prove the leading term for the chromatic number of the random block graph. Joint work with Anders Martinsson, Konstantinos Panagiotou and Miloš Trujić.

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