Duality theorems for stars and combs I: Arbitrary stars and combs
Carl Bürger, Jan Kurkofka · Journal of Graph Theory · 2021
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.