Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9512176 | Discrete Mathematics | 2005 | 9 Pages |
Abstract
It has already been proved that given two closed surfaces F12 and F22 with 2Ï(F12)-Ï(F22)⩾4, there exists a triangulation on F12 which can be embedded on F22 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 2Ï(F12)-Ï(F22)⩾O(g1), 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yusuke Suzuki,