The rectilinear local crossing number of $K_n$
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arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866913353124806656 |
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| author | Ábrego, Bernardo M. Fernández-Merchant, Silvia |
| author_facet | Ábrego, Bernardo M. Fernández-Merchant, Silvia |
| contents | We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin \{8, 14 \}, $ \[ {\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left( n-3-\left\lceil \frac{n-3}{3} \right\rceil \right) \left\lceil \frac{n-3}{3} \right\rceil \right\rceil, \] ${\bar{\rm{lcr}}}(K_8)=4$, and ${\bar{\rm{lcr}}}(K_{14})=15$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1508_07926 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The rectilinear local crossing number of $K_n$ Ábrego, Bernardo M. Fernández-Merchant, Silvia Combinatorics 05C10, 05C62, 52C10, 68R10 We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin \{8, 14 \}, $ \[ {\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left( n-3-\left\lceil \frac{n-3}{3} \right\rceil \right) \left\lceil \frac{n-3}{3} \right\rceil \right\rceil, \] ${\bar{\rm{lcr}}}(K_8)=4$, and ${\bar{\rm{lcr}}}(K_{14})=15$. |
| title | The rectilinear local crossing number of $K_n$ |
| topic | Combinatorics 05C10, 05C62, 52C10, 68R10 |
| url | https://arxiv.org/abs/1508.07926 |