\magnification=1200
\hsize=4in
\overfullrule=0pt
\nopagenumbers
\noindent
%
%
{\bf David Arthur}
%
%
\medskip
\noindent
%
%
{\bf The Restricted Arc-Width of a Graph}
%
%
\vskip 5mm
\noindent
%
%
%
%
An arc-representation of a graph is a function mapping each vertex in
the graph to an arc on the unit circle in such a way that adjacent
vertices are mapped to intersecting arcs. The width of such a
representation is the maximum number of arcs passing through a single
point. The arc-width of a graph is defined to be the minimum width
over all of its arc-representations. We extend the work of Bar\'at and
Hajnal on this subject and develop a generalization we call restricted
arc-width. Our main results revolve around using this to bound
arc-width from below and to examine the effect of several graph
operations on arc-width. In particular, we completely describe the
effect of disjoint unions and wedge sums while providing tight bounds
on the effect of cones.

\bye

.
