\magnification=1200
\hsize=4in
\overfullrule=0pt
\input iansmacros
\nopagenumbers
\noindent
%
%
{\bf Laurent Beaudou and Drago Bokal}
%
%
\medskip
\noindent
%
%
{\bf On the Sharpness of Some Results Relating Cuts and Crossing Numbers}
%
%
\vskip 5mm
\noindent
%
%
%
%
It is already known that for very small edge cuts in graphs, the
crossing number of the graph is at least the sum of the crossing
number of (slightly augmented) components resulting from the cut.
Under stronger connectivity condition in each cut component that was
formalized as a graph operation called zip product, a similar result
was obtained for edge cuts of any size, and a natural question was
asked, whether this stronger condition is necessary.  In this paper,
we prove that the relaxed condition is not sufficient when the size of
the cut is at least four, and we prove that the gap can grow
quadratically with the cut size.



\bye