Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

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

Graphs with the Turan Property

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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