An upper bound on the size of irreducible quadrangulations Gloria Aguilar Cruz and Francisco Javier Zaragoza Martínez

摘要

Let S be a closed surface with Euler genus g. A quadrangulation G of a closed surface S is irreducible if it does not have any contractible face. Nakamoto and Ota gave a linear upper bound for the number n of vertices of G in terms of g. By extending Nakamoto and Ota's method we improve their bound to get that n is no greater than 159.5 g - 46.