Castling tree of tight Dyck nests with applications to odd and middle-levels graphs
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910898419924992 |
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| author | Dejter, Italo J. |
| author_facet | Dejter, Italo J. |
| contents | A subfamily of Dyck words called tight Dyck words is seen to correspond, via a "castling" procedure, to the vertex set of an ordered tree $T$. From $T$, a "blowing" operation recreates the whole family ol Dyck words. The vertices of $T$ can be elementarily updated all along $T$. This simplifies an edge-supplementary arc-factorization view of Hamilton cycles of odd and middle-levels graphs found by T. Mütze et al. This take into account that the Dyck words represent: {\bf(a)} the cyclic and dihedral vertex classes of odd and middle-levels graphs, respectively, and {\bf(b)} the cycles of their 2-factors, as found by T. Mütze et al. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_14249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Castling tree of tight Dyck nests with applications to odd and middle-levels graphs Dejter, Italo J. Combinatorics 05C15, 05C38, 05C75, 68R15 A subfamily of Dyck words called tight Dyck words is seen to correspond, via a "castling" procedure, to the vertex set of an ordered tree $T$. From $T$, a "blowing" operation recreates the whole family ol Dyck words. The vertices of $T$ can be elementarily updated all along $T$. This simplifies an edge-supplementary arc-factorization view of Hamilton cycles of odd and middle-levels graphs found by T. Mütze et al. This take into account that the Dyck words represent: {\bf(a)} the cyclic and dihedral vertex classes of odd and middle-levels graphs, respectively, and {\bf(b)} the cycles of their 2-factors, as found by T. Mütze et al. |
| title | Castling tree of tight Dyck nests with applications to odd and middle-levels graphs |
| topic | Combinatorics 05C15, 05C38, 05C75, 68R15 |
| url | https://arxiv.org/abs/2306.14249 |