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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.12561 |
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| _version_ | 1866917208525897728 |
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| author | Tanaka, Yuuho |
| author_facet | Tanaka, Yuuho |
| contents | We classify weakly connected spanning closed (WCSC) subgraphs of $\overrightarrow{C_n^2}$, the square of a directed $n$-vertex cycle. Then we show that every spanning tree of $\overrightarrow{C_n^2}$ is contained in a unique nontrivial WCSC subgraph of $\overrightarrow{C_n^2}$. As a result, we obtain a purely combinatorial derivation of the formula for the number of directed spanning trees of $\overrightarrow{C_n^2}$. Moreover, we obtain the formula for the number of directed spanning trees of $\overrightarrow{C_n^2}$, which is a Jacobsthal number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12561 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spanning trees in directed square cycles Tanaka, Yuuho Combinatorics We classify weakly connected spanning closed (WCSC) subgraphs of $\overrightarrow{C_n^2}$, the square of a directed $n$-vertex cycle. Then we show that every spanning tree of $\overrightarrow{C_n^2}$ is contained in a unique nontrivial WCSC subgraph of $\overrightarrow{C_n^2}$. As a result, we obtain a purely combinatorial derivation of the formula for the number of directed spanning trees of $\overrightarrow{C_n^2}$. Moreover, we obtain the formula for the number of directed spanning trees of $\overrightarrow{C_n^2}$, which is a Jacobsthal number. |
| title | Spanning trees in directed square cycles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.12561 |