Z-knotted triangulations
Mark Pankov, Adam Tyc · arXiv (Cornell University) · 2017
Let $\Gamma$ be a connected simple finite graph embedded in a connected closed $2$-dimen\-sional surface. A zigzag is a closed path in $\Gamma$, where any two consequent edges lie on the same face and for any three consequent edges the face containing the first and second edges is distinct from the face which contains the second and third. The graph $\Gamma$ is $z$-knotted if it contains a singe zigzag. Such graphs are closely connected to Gauss code problem and have nice homological properties. We show that every triangulation of a connected closed $2$-dimensional surface admits a $z$-knotted shredding.