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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.16635 |
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| _version_ | 1866918453081800704 |
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| author | Kauffman, Louis H. Silver, Daniel S. Williams, Susan G. |
| author_facet | Kauffman, Louis H. Silver, Daniel S. Williams, Susan G. |
| contents | For any cubic graph in a closed orientable surface and a perfect matching, the Penrose-Kauffman polynomial is a sum of chromatic polynomials of a collection of associated graphs. A knot-theoretic perspective affords elementary proofs of old and new results about the polynomial. The Four Color Theorem is shown to be equivalent to a statement about 3-coloring alternating link diagrams in the plane that are reduced and have no bigon regions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16635 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Penrose-Kauffman Polynomial Kauffman, Louis H. Silver, Daniel S. Williams, Susan G. Geometric Topology Primary 05C15, secondary 57M15 For any cubic graph in a closed orientable surface and a perfect matching, the Penrose-Kauffman polynomial is a sum of chromatic polynomials of a collection of associated graphs. A knot-theoretic perspective affords elementary proofs of old and new results about the polynomial. The Four Color Theorem is shown to be equivalent to a statement about 3-coloring alternating link diagrams in the plane that are reduced and have no bigon regions. |
| title | The Penrose-Kauffman Polynomial |
| topic | Geometric Topology Primary 05C15, secondary 57M15 |
| url | https://arxiv.org/abs/2604.16635 |