When a forest, narrowed to an atom of subset algebra, turns out to be a tree
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913692149350400 |
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| author | Buslov, Vasily |
| author_facet | Buslov, Vasily |
| contents | It is proved that the restriction of a $k$ and $(k-1)$-component directed spanning forest of minimal weight to an atom of the subset algebra generated by the sets of vertices of trees of $k$-component minimal spanning forests is a tree. For spanning minimal forests consisting of fewer components, this property, generally speaking, does not exist. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_19068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When a forest, narrowed to an atom of subset algebra, turns out to be a tree Buslov, Vasily Combinatorics 05C20 (Primary) 05C35 (Secondary) G.2.2 It is proved that the restriction of a $k$ and $(k-1)$-component directed spanning forest of minimal weight to an atom of the subset algebra generated by the sets of vertices of trees of $k$-component minimal spanning forests is a tree. For spanning minimal forests consisting of fewer components, this property, generally speaking, does not exist. |
| title | When a forest, narrowed to an atom of subset algebra, turns out to be a tree |
| topic | Combinatorics 05C20 (Primary) 05C35 (Secondary) G.2.2 |
| url | https://arxiv.org/abs/2501.19068 |