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arXiv · 2507.11814

Unavoidable butterfly minors in digraphs of large cycle rank

Meike Hatzel·O-joung Kwon·Myounghwan Lee·Sebastian Wiederrecht
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Abstract

Cycle rank is one of the depth parameters for digraphs introduced by Eggan in 1963. We show that there exists a function $f:\mathbb{N}\to \mathbb{N}$ such that every digraph of cycle rank at least $f(k)$ contains a directed cycle chain, a directed ladder, or a directed tree chain of order $k$ as a butterfly minor. We also investigate a new connection between cycle rank and a directed analogue of the weak coloring number of graphs.

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Meike Hatzel, O-joung Kwon, Myounghwan Lee, Sebastian Wiederrecht. 2025-07-16. Unavoidable butterfly minors in digraphs of large cycle rank. https://arxiv.org/abs/2507.11814

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