2019/02/27 by Kwiatkowski, Mariusz, Pankov, Mark, Tyc, Adam
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.10788
We investigate zigzags in triangulations of connected closed 2-dimensional 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.