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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, February 10, 2004, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Robert Berke

Turan's famous theorem asserts that adding an edge to an r-colorable graph
G with the maximum number of edges (w.r.t its r-colorability) forces not
only to use r+1 colors in a proper coloring but also introduces a K_{r+1}
as a subgraph of it. This fact gives rise to the following property on
graphs:

A graph G satisfies the Turan Property, if for every induced subgraph G'
of G, and every integer r>0, the maximum number of edges in a K_{r+1}-free
subgraph of G' is equal to the maximum number of edges in an r-colorable
subgraph of it.

We will motivate the definition of the Turan Property, show its relation to perfect graphs and prove that line graphs of bipartite graphs satisfy the Turan Property. The results presented in this talk are taken from "Problems and results in Extremal Combinatorics - II" by Noga Alon.

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