@inbook{c39d9041e6a34d8cbb4f3a4fe15e3239,
title = "Constant Congestion Brambles in Directed Graphs",
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, 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.",
keywords = "Directed graphs, Directed treewidth, Graph theory",
author = "Tom{\'a}{\v s} Masa{\v r}{\'i}k and Marcin Pilipczuk and Pawe{\l} Rz{\c a}{\.z}ewski and Manuel Sorge",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2021",
month = jan,
day = "1",
doi = "10.1007/978-3-030-83823-2\_50",
language = "English",
series = "Trends in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "318--324",
booktitle = "Trends in Mathematics",
address = "Germany",
}