10 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…
Coloring digraphs with colors
Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta
The dichromatic number of a digraph is the minimum number of colors needed to partition its vertex set into acyclic subdigraphs. A biclique is a set of vertices inducing all possib…
Edge-colouring and orientations: applications to degree- and -boundedness
Arnab Char, Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta
We prove a new generalisation of Ramsey's theorem by showing that every -edge-coloured graph with sufficiently large minimum degree contains a monochromatic induced subgraph who…
Accelerating Scientific Research with Gemini: Case Studies and Common Techniques
David P. Woodruff, Vincent Cohen-Addad, Lalit Jain +33
Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks,…
A quasi-polynomial bound for the minimal excluded minors for a surface
Sarah Houdaigoui, Ken-ichi Kawarabayashi
As part of their graph minor project, Robertson and Seymour showed in 1990 that the class of graphs that can be embedded in a given surface can be characterized by a finite set of…
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-ordere…