CONSTANT CONGESTION BRAMBLES in DIRECTED GRAPHS

Tomáš Masařík, Marcin Pilipczuk, Paweł Rzążewski, Manuel Sorge

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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, was proved in 2015 by Kawarabayashi and Kreutzer. However, the function f obtained in the proof is very fast growing. In this work, we show that if one relaxes directed grid to bramble of constant congestion, one can obtain a polynomial bound. More precisely, we show that for every k ≥ 1 there exists t = O(k48 log13 k) 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
Pages (from-to)922-938
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Volume36
Issue number2
DOIs
StatePublished - 1 Jan 2022
Externally publishedYes

Keywords

  • bramble
  • directed graph
  • directed treewidth

ASJC Scopus subject areas

  • General Mathematics

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