ACO The ACO Seminar (2011-2012)

Apr 12, 3:30pm, Wean 8220
Tobias Mueller, CWI Amsterdam
Line arrangements and geometric representations of graphs


A dot product representation of a graph assigns to each vertex s a vector v(s) in R^k in such a way that v(s)^T v(t) > 1 if and only st is an edge. Similarly, in a distance representation |v(s)-v(t)| < 1 if and only if st is an edge.

I will discuss the solution of some open problems by Spinrad, Breu&Kirkpatrick and others on these and related geometric representations of graphs.

The proofs make use of a connection to oriented pseudoline arrangements, some results from algebraic geometry and the Colin de Verdiere parameter.

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