A star-comb lemma for finite digraphs
Abstract
It is well-known that for any set $U$ of vertices in a connected graph $G$ there is either a subdivided star in $G$ with a large number of leaves in $U$, or a comb in $G$ with a large number of teeth in $U$. In this paper we extend this property to directed graphs. More precisely, we prove that for any set $U$ of vertices in a strongly connected directed graph $D$, there exists a strongly connected substructure of $D$ attached to a large number of vertices in $U$ that is either shaped by a star or shaped by a comb.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.03883
- arXiv:
- arXiv:2406.03883
- Bibcode:
- 2024arXiv240603883R
- Keywords:
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- Mathematics - Combinatorics;
- 05C20;
- 05C40
- E-Print:
- 15 pages, 11 figures