Skewness, crossing number and Euler's bound for graphs on surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910773509357568 |
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| author | Kainen, Paul C. |
| author_facet | Kainen, Paul C. |
| contents | For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $δ_S(G) \leq μ_S(G) \leq ν_S(G)$, where $μ$ and $ν$ denote skewness and crossing number and $δ$ is the Euler-formula lower bound. Recent developments are surveyed; new results are given for the ``folded'' cube including its genus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Skewness, crossing number and Euler's bound for graphs on surfaces Kainen, Paul C. Combinatorics 05C10, 05C62, 57K20 For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $δ_S(G) \leq μ_S(G) \leq ν_S(G)$, where $μ$ and $ν$ denote skewness and crossing number and $δ$ is the Euler-formula lower bound. Recent developments are surveyed; new results are given for the ``folded'' cube including its genus. |
| title | Skewness, crossing number and Euler's bound for graphs on surfaces |
| topic | Combinatorics 05C10, 05C62, 57K20 |
| url | https://arxiv.org/abs/2501.02400 |