\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 Yan Yang and Yanpei Liu}
%
%
\medskip
\noindent
%
%
{\bf Flexibility of Embeddings of Bouquets of Circles on the Projective Plane and Klein Bottle}
%
%
\vskip 5mm
\noindent
%
%
%
%
In this paper, we study the flexibility of embeddings of bouquets
of circles on the projective plane and the Klein bottle. The
numbers (of equivalence classes) of embeddings of bouquets of
circles on these two nonorientable surfaces are obtained in
explicit expressions. As their applications, the numbers (of
isomorphism classes) of rooted one-vertex maps on these two
nonorientable surfaces are deduced.
\bye