A Cantor-Bernstein-type theorem for spanning trees in infinite graphs
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866910458232963072 |
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| author | Erde, Joshua Gollin, Pascal Joó, Atilla Knappe, Paul Pitz, Max |
| author_facet | Erde, Joshua Gollin, Pascal Joó, Atilla Knappe, Paul Pitz, Max |
| contents | We show that if a graph admits a packing and a covering both consisting of $λ$ many spanning trees, where $λ$ is some infinite cardinal, then the graph also admits a decomposition into $λ$ many spanning trees. For finite $λ$ the analogous question remains open, however, a slightly weaker statement is proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_09338 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Cantor-Bernstein-type theorem for spanning trees in infinite graphs Erde, Joshua Gollin, Pascal Joó, Atilla Knappe, Paul Pitz, Max Combinatorics 05C63, 05C40 We show that if a graph admits a packing and a covering both consisting of $λ$ many spanning trees, where $λ$ is some infinite cardinal, then the graph also admits a decomposition into $λ$ many spanning trees. For finite $λ$ the analogous question remains open, however, a slightly weaker statement is proved. |
| title | A Cantor-Bernstein-type theorem for spanning trees in infinite graphs |
| topic | Combinatorics 05C63, 05C40 |
| url | https://arxiv.org/abs/1907.09338 |