Counterexamples regarding linked and lean tree-decompositions of infinite graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918094256996352 |
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| author | Albrechtsen, Sandra Jacobs, Raphael W. Knappe, Paul Pitz, Max |
| author_facet | Albrechtsen, Sandra Jacobs, Raphael W. Knappe, Paul Pitz, Max |
| contents | Kriz and Thomas showed that every (finite or infinite) graph of tree-width $k \in \mathbb{N}$ admits a lean tree-decomposition of width $k$. We discuss a number of counterexamples demonstrating the limits of possible generalisations of their result to arbitrary infinite tree-width.
In particular, we construct a locally finite, planar, connected graph that has no lean tree-decomposition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counterexamples regarding linked and lean tree-decompositions of infinite graphs Albrechtsen, Sandra Jacobs, Raphael W. Knappe, Paul Pitz, Max Combinatorics 05C63, 05C05, 05C83, 05C40 Kriz and Thomas showed that every (finite or infinite) graph of tree-width $k \in \mathbb{N}$ admits a lean tree-decomposition of width $k$. We discuss a number of counterexamples demonstrating the limits of possible generalisations of their result to arbitrary infinite tree-width. In particular, we construct a locally finite, planar, connected graph that has no lean tree-decomposition. |
| title | Counterexamples regarding linked and lean tree-decompositions of infinite graphs |
| topic | Combinatorics 05C63, 05C05, 05C83, 05C40 |
| url | https://arxiv.org/abs/2405.06755 |