Polynomial invariants of cyclically ordered graphs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911270179962880 |
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| author | Bratch, Paul Ellingham, M. N. Ellis-Monaghan, Joanna A. Moffatt, Iain Moltmaker, Wout |
| author_facet | Bratch, Paul Ellingham, M. N. Ellis-Monaghan, Joanna A. Moffatt, Iain Moltmaker, Wout |
| contents | Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biology. We develop a formal theory of cogs and establish a number of invariants of cogs. In particular we detail several ways to present cogs and detail how these descriptions can be used to construct cog invariants by adapting the matching, transition and Yamada polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial invariants of cyclically ordered graphs Bratch, Paul Ellingham, M. N. Ellis-Monaghan, Joanna A. Moffatt, Iain Moltmaker, Wout Combinatorics 05C10, 05C31 Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biology. We develop a formal theory of cogs and establish a number of invariants of cogs. In particular we detail several ways to present cogs and detail how these descriptions can be used to construct cog invariants by adapting the matching, transition and Yamada polynomials. |
| title | Polynomial invariants of cyclically ordered graphs |
| topic | Combinatorics 05C10, 05C31 |
| url | https://arxiv.org/abs/2511.13302 |