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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2503.18700 |
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| _version_ | 1866913754346684416 |
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| author | Beluhov, Nikolai |
| author_facet | Beluhov, Nikolai |
| contents | A leaper is a chess piece which generalises the knight. Given $n$ and a $(p, q)$-leaper $L$, we study the greatest $m$ such that the $m \times m$ grid graph can be embedded into the $n \times n$ leaper graph of $L$. We can assume that $p$ and $q$ are relatively prime. We show that $m \approx n$ when $p$ and $q$ are of opposite parities and $m \approx n/2$ otherwise. The latter case is substantially more difficult. The proof involves certain combinatorial-geometric results on the chords of connected figures which might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Leaper Embeddings Beluhov, Nikolai Combinatorics 05C60 A leaper is a chess piece which generalises the knight. Given $n$ and a $(p, q)$-leaper $L$, we study the greatest $m$ such that the $m \times m$ grid graph can be embedded into the $n \times n$ leaper graph of $L$. We can assume that $p$ and $q$ are relatively prime. We show that $m \approx n$ when $p$ and $q$ are of opposite parities and $m \approx n/2$ otherwise. The latter case is substantially more difficult. The proof involves certain combinatorial-geometric results on the chords of connected figures which might be of independent interest. |
| title | Leaper Embeddings |
| topic | Combinatorics 05C60 |
| url | https://arxiv.org/abs/2503.18700 |