Abstract
Extending the well-known star–comb lemma for infinite graphs, we characterise the graphs that do not contain an infinite comb or an infinite star, respectively, attached to a given set of vertices. We offer several characterisations: in terms of normal trees, tree-decompositions, ranks of rayless graphs and tangle-distinguishing separators.
Original language | English |
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Pages (from-to) | 525-554 |
Number of pages | 30 |
Journal | Journal of Graph Theory |
Volume | 99 |
Issue number | 4 |
Early online date | 21 Jun 2021 |
DOIs | |
Publication status | Published - Apr 2022 |
Keywords
- critical vertex set
- duality
- normal tree
- rank
- stars and combs
- star–comb lemma
- tree-decomposition