11 papers
A directed flat wall theorem excluding a crossrow grid
Meike Hatzel, Ken-ichi Kawarabayashi, Stephan Kreutzer +1
The graph minor project contains the most influential results in recent undirected graph theory research. There has been progress in recent years in generalising some of their resu…
Optimal Bounds for the k-Disjoint Paths Problem
Dario Cavallaro, Maximilian Gorsky, Stephan Kreutzer +2
The Graph Minors Series of Robertson and Seymour forms the foundation of algorithmic structural graph theory, yielding fixed-parameter algorithms for problems such as Disjoint Path…
Well-Quasi-Ordering Eulerian Digraphs: Bounded Carving Width
Dario Cavallaro, Ken-ichi Kawarabayashi, Stephan Kreutzer
We prove that every class of Eulerian directed graphs of bounded carving width (equivalently of bounded degree and treewidth) is well-quasi-ordered by strong immersion. In fact, we…
Cycles of Well-Linked Sets II: an Elementary Bound for the Directed Grid Theorem
Meike Hatzel, Stephan Kreutzer, Marcelo Garlet Milani +1
In 2015, Kawarabayashi and Kreutzer proved the Directed Grid Theorem - the generalisation of the well-known Excluded Grid Theorem to directed graphs - confirming a conjecture by Re…
Well-Quasi-Ordering Eulerian Digraphs Embeddable in Surfaces by Strong Immersion
Dario Cavallaro, Ken-ichi Kawarabayashi, Stephan Kreutzer
We prove that for every surface , the class of Eulerian directed graphs that are Eulerian embeddable into (in particular they have degree at most ) is well-quasi-ordered…
The Directed Disjoint Paths Problem with Congestion
Matthias Bentert, Dario Cavallaro, Amelie Heindl +3
The classic result by Fortune, Hopcroft, and Wyllie [TCS~'80] states that the directed disjoint paths problem is NP-complete even for two pairs of terminals. Extending this well-kn…
Directed treewidth is closed under taking butterfly minors
Gunwoo Kim, Meike Hatzel, Stephan Kreutzer
Butterfly minors are a generalisation of the minor containment relation for undirected graphs to directed graphs. Many results in directed structural graph theory use this notion a…
Generating strongly 2-connected digraphs
Meike Hatzel, Stephan Kreutzer, Evangelos Protopapas +3
We prove that there exist four operations such that given any two strongly -connected digraphs and where is a butterfly-minor of , there exists a sequence $D_0,\d…
Cycles of Well-Linked Sets I: an Elementary Bound for Directed Cycle Packing
Meike Hatzel, Stephan Kreutzer, Marcelo Garlet Milani +1
In 1996, Reed, Robertson, Seymour and Thomas [Combinatorica 1996] proved Younger's Conjecture, which states that, for all directed graphs , there exists a function such that…
Edge-Disjoint Paths in Eulerian Digraphs
Dario Cavallaro, Ken-ichi Kawarabayashi, Stephan Kreutzer
Disjoint paths problems are among the most prominent problems in combinatorial optimization. The edge- as well as vertex-disjoint paths problem, are NP-complete on directed and und…
Packing even directed circuits quarter-integrally
Maximilian Gorsky, Ken-ichi Kawarabayashi, Stephan Kreutzer +1
We prove the existence of a computable function such that for every integer and every digraph either contains a collection of…