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doi:10.1016/j.disc.2004.12.025 
Copyright © 2005 Elsevier B.V. All rights reserved.
Triangulations on closed surfaces which quadrangulate other surfaces II
Yusuke Suzuki
Received 19 December 2002;
revised 3 September 2003;
accepted 8 December 2004.
Available online 27 October 2005.
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Abstract
It has already been proved that given two closed surfaces and
with
, there exists a triangulation on
which can be embedded on
as a quadrangulation. In this paper we refine that result, showing that there exists an integer g0 such that for any two closed surfaces with genus g1
g0 and genus g2 satisfying , there exists a triangulation of the first surface which can be re-embedded on the second as a quadrangulation. Moreover, on the right-hand side of the inequality, we obtain a concrete expression which is asymptotically O(g1). We also obtain similar results for non-orientable surfaces.
Keywords: Triangulation; Quadrangulation; Complete graph
