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 |
|---|---|
| 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