REGULAR TRIANGULATIONS OF NONCOMPACT SURFACES

A triangulation of a surface is delta-regular if each vertex is contained in exactly delta-edges. For each delta greater-than-or-equal-to 7, delta-regular triangulations of arbitrary non-compact surfaces of finite genus are constructed. It is also shown that for delta less-than-or-equal-to 6 there is a delta-regular triangulation of a non-compact surface SIGMA if and only if delta = 6 and SIGMA is homeomorphic to one of the following surfaces: the Euclidean plane, the two-way-infinite cylinder, or the open Mobius band.