Counterexamples regarding linked and lean tree-decompositions of infinite graphs
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...
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| Sprache: | eng |
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| Zusammenfassung: | 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. |
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| DOI: | 10.48550/arxiv.2405.06755 |