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%van der Holst
%Hein","H.v.d.Holst@tue.nl","
\section{Computing the minimum rank of partial $2$-trees} By {\sl Hein van der Holst}.  

\medskip  \noindent A $2$-tree is recursively defined as follows: the complete graph on three vertices is a $2$-tree, and if we have a $2$-tree, a larger can be obtained by adding a new vertex adjacent to the endpoints of an edge in the $2$-tree. A partial $2$-tree is a subgraph of a $2$-tree. The minimum rank of a graph $G$ is the smallest rank over all symmetric matrices $A=[a_{i,j}]$ with $a_{i,j}\not=0, i\not=j$ if and only if $ij$ is an edge of $G$. In this talk, I present an efficient algorithm to compute the minimum rank of a partial $2$-tree, and show how it can be extended to compute other minimum rank-type problems.
%minimum rank, symmetric matrix, algorithm, $k$-trees","15A03","68A10","","05:52:43","Tue Mar 25 2008","131.155.70.6"
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