Abstract :
It has already been proved that given two closed surfaces image and image with image, there exists a triangulation on image which can be embedded on image as a quadrangulation. In this paper we refine that result, showing that there exists an integer image such that for any two closed surfaces with genus image and genus image satisfying image, 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 image. We also obtain similar results for non-orientable surfaces.
