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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, March 07, 2006, 12:15 pm

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

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

**Speaker**: Konstantinos Panagiotou

For a graph G, let ET(G) denote the maximum number of edges in a triangle-free subgraph (not necessarily induced) of G, and let EB(G) be the maximum number of edges in a bipartite subgraph of G.

Of course, we always have ET(G) ≥ EB(G), but the general intuition -- guided by various known results -- suggests that, for dense enough graphs, these two parameters will typically be equal.

In 1990, Babai, Simonovits and Spencer studied these parameters for random graphs G(n,p) and confirmed this intuition for dense graphs. In particular, they proved that there is a (small) positive constant c such that, for p ≥ 1/2 - c, with high probability we have ET(G(n,p)) = EB(G(n,p)).

Babai, Simonovits and Spencer asked whether this result could be extended to
cover all constant values of p. In this talk we answer this question
affirmatively and show that the above property in fact holds whenever
p=p(n) ≥ n^{-c}, for some fixed c > 0.

This is joint work with Graham Brightwell and Angelika Steger.

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