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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00375 |
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| _version_ | 1866918532584833024 |
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| author | Sun, Timothy |
| author_facet | Sun, Timothy |
| contents | Complementing a theorem of Škrekovski, we characterize the $(h-1)$-critical graphs embeddable in surfaces of Euler genus at least $5$, where $h$ denotes the Heawood number of the surface. Outside of a few small cases, the bulk of our proof is determining the genus of the join of a complete graph and the 5-cycle. As a byproduct of our proof, we also provide a simpler solution to the minimum triangulations problem for nonorientable surfaces using the theory of current graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00375 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Embeddings of critical graphs near the Heawood bound Sun, Timothy Combinatorics Complementing a theorem of Škrekovski, we characterize the $(h-1)$-critical graphs embeddable in surfaces of Euler genus at least $5$, where $h$ denotes the Heawood number of the surface. Outside of a few small cases, the bulk of our proof is determining the genus of the join of a complete graph and the 5-cycle. As a byproduct of our proof, we also provide a simpler solution to the minimum triangulations problem for nonorientable surfaces using the theory of current graphs. |
| title | Embeddings of critical graphs near the Heawood bound |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2606.00375 |