Constant Congestion Brambles in Directed Graphs

Tomáš Masařík, Marcin Pilipczuk, Paweł Rzążewski, Manuel Sorge

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


The Directed Grid Theorem, stating that there is a function f such that a directed graph of directed treewidth at least f(k) contains a directed grid of size at least k as a butterfly minor, after being a conjecture for nearly 20 years, has been proven in 2015 by Kawarabayashi and Kreutzer. However, the function f in the proof is very fast growing. Here, we show that if we relax directed grid to bramble of constant congestion, we obtain a polynomial bound. More precisely, we show that for every k≥ 1 there exists t= O(k48log13k) such that every directed graph of directed treewidth at least t contains a bramble of congestion at most 8 and size at least k.

Original languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages7
StatePublished - 1 Jan 2021
Externally publishedYes

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


  • Directed graphs
  • Directed treewidth
  • Graph theory

ASJC Scopus subject areas

  • Mathematics (all)


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