Raphael W. Jacobs

About me

I am a 4th year PhD student working in structural graph theory under the supervision of Reinhard Diestel. My main research interests include tangles, decompositions of graphs, graph minors, connectivity and applications in cluster analysis.

Research

• A structural duality for path-decompositions into parts of small radius (with Sandra Albrechtsen, Reinhard Diestel, Ann-Kathrin Elm, Eva Fluck, Paul Knappe and Paul Wollan), 2023, submitted. (arXiv)
• Menger's Theorem in bidirected graphs (with Nathan Bowler, Ebrahim Ghorbani, Florian Gut and Florian Reich), 2023, submitted. (arXiv)
• The induced two paths problem (with Sandra Albrechtsen, Tony Huynh, Paul Knappe and Paul Wollan), 2023, submitted. (arXiv)
• Efficiently distinguishing all tangles in locally finite graphs (with Paul Knappe), 2023, submitted. (arXiv)
• A grid theorem for strong immersions of walls (with Reinhard Diestel, Paul Knappe and Paul Wollan), 2023, submitted. (arXiv)
• Canonical graph decompositions via coverings (with Reinhard Diestel, Paul Knappe and Jan Kurkofka), 2022, submitted. (arXiv)
• The Lovász-Cherkassky theorem for locally finite graphs with ends (with Attila Joó, Paul Knappe, Jan Kurkofka and Ruben Melcher), Discrete Mathematics, Volume 346, Issue 12, 2023, 113586. (Journal, arXiv)
• Point sets and functions inducing tangles of set separations (with Reinhard Diestel and Christian Elbracht), to appear in Journal of Combinatorics. (arXiv)

Theses

• How to build a tree of tangles by local refinements, 2020, MSc dissertation. (PDF)

Teaching

• Summer semester 2023: Exercise class to Graph Theory I by Nathan Bowler.
• Winter semester 2020/21: Exercise class to Mathematics I for Computer Scientists by Stefan Geschke.