Raphael W. Jacobs

Fachbereich Mathematik
Bereich DM
Bundesstraße 55 (Geomatikum)
20146 Hamburg

Raum 232
Tel.: +49 40 42838-5159
E-Mail: raphael.jacobs (at) uni-hamburg.de
Office hours: by appointment

About me

I am a 5th year PhD student working in structural graph theory under the supervision of Reinhard Diestel. My main research interests include decompositions of graphs, tangles, graph minors and connectivity.

Research

Local-Global Graph Decompositions

Locally chordal graphs (with Tara Abrishami, Paul Knappe and Jonas Kobler), 2025. (arXiv)

Canonical graph decompositions and local separations: From infinite coverings to a finite combinatorial theory (with Johannes Carmesin, Paul Knappe and Jan Kurkofka), 2025. (arXiv)

Canonical graph decompositions via coverings (with Reinhard Diestel, Paul Knappe and Jan Kurkofka), to appear in Transactions of the American Mathematical Society (TAMS). (arXiv)

Tangles

On vertex sets inducing tangles (with Sandra Albrechtsen, Hanno von Bergen, Paul Knappe and Paul Wollan), 2024, submitted. (arXiv)

Efficiently distinguishing all tangles in locally finite graphs (with Paul Knappe), Journal of Combinatorial Theory, Series B, Volume 167, Pages 189-214. (Journal, arXiv)

Point sets and functions inducing tangles of set separations (with Reinhard Diestel and Christian Elbracht), Journal of Combinatorics, Volume 15, Number 3, Pages 283-306. (Journal, arXiv)

Coarse Graph Theory

A characterisation of graphs quasi-isometric to K₄-minor-free graphs (with Sandra Albrechtsen, Paul Knappe and Paul Wollan), 2024, submitted. (arXiv)

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. (arXiv)

A Menger-type theorem for two induced paths (with Sandra Albrechtsen, Tony Huynh, Paul Knappe and Paul Wollan), SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Pages 1438-1450. (Journal, arXiv)

Connectivity and Tree-Structure

Hitting cycles through prescribed vertices or edges (with Nathan Bowler, Ebrahim Ghorbani, Florian Gut and Florian Reich), 2024, submitted. (arXiv)

Linked tree-decompositions into finite parts (with Sandra Albrechtsen, Paul Knappe and Max Pitz), 2024, submitted. (arXiv)

Counterexamples regarding linked and lean tree-decompositions of infinite graphs (with Sandra Albrechtsen, Paul Knappe and Max Pitz), Journal of Graph Theory. (Journal, arXiv)

Menger's Theorem in bidirected graphs (with Nathan Bowler, Ebrahim Ghorbani, Florian Gut and Florian Reich), 2023, submitted. (arXiv)

A grid theorem for strong immersions of walls (with Reinhard Diestel, Paul Knappe and Paul Wollan), Journal of Graph Theory, 110, Pages 23-32. (Journal, 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, 113586. (Journal, 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.

Links

You can find my articles on arXiv, my Google Scholar profile and my ORCID.