\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf S. D. Noble}
%
%
\medskip
\noindent
%
%
{\bf Evaluating a Weighted Graph Polynomial for Graphs of Bounded Tree-Width}
%
%
\vskip 5mm
\noindent
%
%
%
%
We show that for any $k$ there is a polynomial time algorithm to
evaluate the weighted graph polynomial $U$ of any graph with
tree-width at most $k$ at any point. For a graph with $n$ vertices,
the algorithm requires $O(a_k n^{2k+3})$ arithmetical operations,
where $a_k$ depends only on $k$.



\bye