Triangulations with homogeneous zigzags
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2019
- DOI:
- 10.48550/arXiv.1902.10788
- arXiv:
- arXiv:1902.10788
- Bibcode:
- 2019arXiv190210788K
- Keywords:
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- Mathematics - Combinatorics