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Raphael W. Jacobs

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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

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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 tangles, decompositions of graphs, graph minors and connectivity.

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Research

• A characterisation of graphs quasi-isometric to K₄-minor-free graphs (with Sandra Albrechtsen, Paul Knappe and Paul Wollan), 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), 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, 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), SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Pages 1438-1450. (Journal, 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)
• 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, 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)

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Theses

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

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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.

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Links

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

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