\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
\nopagenumbers
\noindent
%
%
\def\vt{t\kern-0.22em\raise.18ex\hbox{\char'47}\lower.18ex\hbox{}\kern-0.08em}{\bf\'Eva Czabarka, Ondrej S\'ykora, L\'aszl\'o A. Sz\'ekely and Imrich Vr{\vt}o}
%
%
\medskip
\noindent
%
%
{\bf Outerplanar Crossing Numbers, the Circular Arrangement Problem and
Isoperimetric Functions }
%
%
\vskip 5mm
\noindent
%
%
%
%
We extend a lower bound due to Shahrokhi, S\'ykora, Sz\'ekely and
Vr{\vt}o for the outerplanar crossing number (in other terminologies
also called convex, circular and one-page book crossing number) to a
more general setting. In this setting we can show a better lower bound
for the outerplanar crossing number of hypercubes than the best lower
bound for the planar crossing number. We exhibit further sequences of
graphs, whose outerplanar crossing number exceeds by a factor of $\log
n$ the planar crossing number of the graph. We study the circular
arrangement problem, as a lower bound for the linear arrangement
problem, in a general fashion. We obtain new lower bounds for the
circular arrangement problem. All the results depend on establishing
good isoperimetric functions for certain classes of graphs. For
several graph families new near-tight isoperimetric functions are
established.
\bye