\begin{thebibliography}{10}

\bibitem{CHAR86}
G.~Chartrand and L.~Lesniak.
\newblock {\em Graphs and Digraphs}.
\newblock Wadsworth \& Brooks/Cole Advanced Books \& Software, Monterey, CA,
  2nd. edition, 1986.

\bibitem{cottingham:dissertation}
J.E. Cottingham.
\newblock {\em Thrackles, Surfaces, and Maximum Drawing of Graphs}.
\newblock PhD thesis, Clemson, University, Clemson, SC 29634, August 1993.

\bibitem{dyck:1888}
W.~Dyck.
\newblock Beitr\"{a}ge zur analysis situs.
\newblock {\em Math. Ann.}, 32:457--512, 1888.

\bibitem{edmonds:1960}
J.~Edmonds.
\newblock A combinatorial representation for polyhedral surfaces.
\newblock {\em Notices Amer. Math. Soc.}, 7:646, 1960.

\bibitem{eg:cnog}
P.~Erd\"{o}s and R.~Guy.
\newblock Crossing numbers of graphs.
\newblock In et~al. Alavi, editor, {\em Graph Theory and Applications}, pages
  111--124. Springer-Verlag, New York, 1973.

\bibitem{gj83:cninpc}
M.R. Garey and D.S. Johnson.
\newblock Crossing number is np-complete.
\newblock {\em SIAM J. of Alg. Disc. Meth.}, 4:312--316, 1983.

\bibitem{GUY72}
R.K. Guy.
\newblock A minimal problem concerning complete plane graphs.
\newblock In Y.~Alavi, D.R. Lick, and A.T. White, editors, {\em Graph Theory
  and Applications}, pages 111--124, Berlin, 1972. Springer-Verlag.

\bibitem{heffter:1891}
L.~Heffter.
\newblock \"{U}ber das problem der nachbargebiete.
\newblock {\em Math. Ann.}, 38:477--508, 1891.

\bibitem{lovegrove:masters}
C.~Lovegrove.
\newblock Crossing numbers of permutation graphs.
\newblock Master's thesis, Clemson University, Clemson, SC 29634, May 1988.

\bibitem{lr:cnopg}
C.~Lovegrove and R.D. Ringeisen.
\newblock Crossing numbers of permutation graphs.
\newblock {\em Congr. Numer.}, 67:125--135, 1988.

\bibitem{th96:apsoaffmormcp}
J.T. Thorpe and F.C. Harris, Jr.
\newblock A parallel stochastic optimization algorithm for finding mappings of
  the rectilinear minimal crossing problem.
\newblock {\em Ars Comb.}, {\it to appear}.

\bibitem{turan:1977}
P.~Turan.
\newblock A note of welcome.
\newblock {\em Journal of Graph Theory}, 1:7--9, 1977.

\bibitem{youngs63:miatgoag}
J.W.T. Youngs.
\newblock Minimal imbeddings and the genus of a graph.
\newblock {\em J. Math. Mech.}, 12:303--315, 1963.

\end{thebibliography}
