Triangulations with homogeneous zigzags

Abstract

We investigate zigzags in triangulations of connected closed 2dimensional surfaces and show that there is a one-to-one correspondence between triangulations with homogeneous zigzags and closed 2-cell embeddings of directed Eulerian graphs in surfaces. A triangulation is called z-knotted if it has a single zigzag. We construct a family of tree structured z-knotted spherical triangulations whose zigzags are homogeneous.