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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, December 07, 2006, 12:15 pm

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

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

**Speaker**: Rico Zenklusen

Let G=(V,E,w) be a complete graph with n vertices and distinct positive edge
weights w. We fix a constant k \in {1,2,...,n-1}. For any subset of vertices
X of V with cardinality k-1 we denote by MST(G\X) the set of edges contained
in the minimum spanning tree in the subgraph G[V\X]. Goemans and Vondrak
observed that many edges in G have the property that they are not contained
in any minimum spanning tree of the form MST(G\X) where X is as described
above. More precisely let M_k be the set of edges contained in any minimum
spanning tree of the form MST(G\X), i.e. M_k=\cup_{X\subseteq V,
|X|=k-1} MST(G\X).

Goemans and Vondrak made the following conjecture:
|M_k| <= n*k-0.5*(k+1)*k.

A proof of this conjecture will be presented in this talk.

Joint work with Gregory B. Sorkin and Angelika Steger.

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