Duality theorems for stars and combs I: Arbitrary stars and combs
arXiv:2004.00594 · doi:10.1002/jgt.22706
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.
27 pages, 1 figure