Partial triangulations of surfaces with girth constraints
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915053810221056 |
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| author | Power, Stephen C. |
| author_facet | Power, Stephen C. |
| contents | Barnette and Edelson have shown that there are finitely many minimal triangulations of a connected compact 2-manifold M. Similar finiteness results are obtained for cellular partial triangulations that satisfy various girth inequality constraints for embedded cycles. A characterisation of various M-embedded sparse graphs is given in terms of the satisfaction of higher genus girth inequalities. With this it is shown that there are finitely many contraction-minimal M-embedded graphs that are (3,6)-tight or (3,3)-tight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Partial triangulations of surfaces with girth constraints Power, Stephen C. Geometric Topology Combinatorics math.GT Barnette and Edelson have shown that there are finitely many minimal triangulations of a connected compact 2-manifold M. Similar finiteness results are obtained for cellular partial triangulations that satisfy various girth inequality constraints for embedded cycles. A characterisation of various M-embedded sparse graphs is given in terms of the satisfaction of higher genus girth inequalities. With this it is shown that there are finitely many contraction-minimal M-embedded graphs that are (3,6)-tight or (3,3)-tight. |
| title | Partial triangulations of surfaces with girth constraints |
| topic | Geometric Topology Combinatorics math.GT |
| url | https://arxiv.org/abs/2309.10638 |