English

Duality theorems for stars and combs I: Arbitrary stars and combs

Combinatorics 2021-08-09 v3

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.

Keywords

Cite

@article{arxiv.2004.00594,
  title  = {Duality theorems for stars and combs I: Arbitrary stars and combs},
  author = {Carl Bürger and Jan Kurkofka},
  journal= {arXiv preprint arXiv:2004.00594},
  year   = {2021}
}

Comments

27 pages, 1 figure

R2 v1 2026-06-23T14:35:43.499Z