Hamburg papers on

Tree-of-tangle theorems: in graphs, matroids, and abstract separation systems

• Locally chordal graphs (T. Abrishami, R. W. Jacobs, P. Knappe, J. Kobler), preprint 2025; ArXiv
• Canonical graph decompositions and local separations: From infinite coverings to a finite combinatorial theory (J. Carmesin, R. W. Jacobs, P. Knappe, J. Kurkofka), preprint 2025; ArXiv
• Refining tree-decompositions so that they display the k-blocks (S. Albrechtsen), preprint 2024; ArXiv
• Optimal trees of tangles: refining the essential parts (S. Albrechtsen), preprint 2023; ArXiv
• Efficiently distinguishing all tangles in locally finite graphs (R. Jacobs and P. Knappe), Journal of Combinatorial Theory B 167 (2024), 189-214; ArXiv
• Refining trees of tangles in abstract separation systems I: Inessential parts (S. Albrechtsen), preprint 2023; ArXiv 
• Canonical graph decompositions via coverings (R. Diestel, R. Jacobs, P. Knappe and J. Kurkofka), preprint 2022; ArXiv
• Edge-connectivity and tree-structure in finite and infinite graphs (C. Elbracht, J. Kurkofka and M. Teegen), preprint 2020; ArXiv 
• Obtaining trees of tangles from tangle-tree duality (C. Elbracht, J. Kneip and M. Teegen), J. Combinatorics 13 (2022), 251-287; ArXiv 
• A canonical tree-of-tangles theorem for structurally submodular separation systems (C. Elbracht and J. Kneip), Combinatorial Theory 1 (2021); ArXiv 
• A tree-of-tangles theorem for infinite-order tangles in graphs (A. Elm & J. Kurkofka), Abhandlungen aus dem Mathematischen Seminar der UHH 92 (2022), 139–178; ArXiv 
• Canonical trees of tree-decompositions (J. Carmesin, M. Hamann & B. Miraftab), JCTB 152 (2022), 1-26; ArXiv 
• Trees of tangles in infinite separation systems (C. Elbracht, J. Kneip and M. Teegen), Mathematical Proceedings of the Cambridge Philosophical Society 173(2) (2022); ArXiv 
• Trees of tangles in abstract separation systems (C. Elbracht, J. Kneip and M. Teegen), JCTA 180 (2021), 105425; ArXiv 
• Structural submodularity and tangles in abstract separation systems (R. Diestel, J. Erde and D. Weißauer), JCTA 167C (2019), 155-180; PDF 
• All graphs have tree-decompositions displaying their topological ends (J. Carmesin), Combinatorica 39 (2019), 545–596; PDF 
• Profiles of separations: in graphs, matroids and beyond (R. Diestel, F. Hundertmark and S. Lemanczyk), Combinatorica 39 (2019), 37–75; PDF 
• A short proof that every finite graph has a tree-decomposition displaying its tangles (J. Carmesin), European J. Combin. 58 (2016), 61–65; PDF 
• Refining a tree-decomposition which distinguishes tangles (J. Erde), SIAM Journal on Discrete Mathematics 31 (2017), 1529–1551; ArXiv 
• Ends and tangles (R. Diestel), Abhandlungen Math. Sem. Univ. Hamburg 87 (2017), 223–244; PDF 
• Canonical tree-decompositions of a graph that display its k-blocks (J. Carmesin and P. Gollin), JCTB 122 (2017), 1-20; ArXiv 
• Canonical tree-decompositions of finite graphs I. Existence and algorithms (J. Carmesin, R. Diestel, M. Hamann and F. Hundertmark), JCTB 116 (2016), 1–24; PDF 
• Canonical tree-decompositions of finite graphs II. Essential parts (J. Carmesin, R. Diestel, M. Hamann and F. Hundertmark), JCTB 118 (2016), 268–283; PDF 
• Profiles. An algebraic approach to combinatorial connectivity (Fabian Hundertmark), preprint 2011; ArXiv 
• Connectivity and tree-structure in finite graphs (J. Carmesin, R. Diestel, F. Hundertmark and M. Stein), Combinatorica 34 (2014), 1–35; PDF 

Some theses in the area:

• Distinguishing and witnessing dense structures in graphs and abstract separation systems (C. Elbracht), PhD dissertation, Hamburg 2021; PDF 
• Tangles, Trees of Tangles, and Submodularity (M. Teegen), PhD dissertation, Hamburg 2021; PDF 
• Describing highly cohesive structures in the plane via tangles (H. v.Bergen), Bachelorarbeit Hamburg 2020; PDF 
• Tangles and where to find them (J. Kneip), PhD dissertation, Hamburg 2020; PDF 
• How to build a tree of tangles by local refinements (R. Jacobs), MSc dissertation, Hamburg 2020; PDF 
• Tangles auf triangulierten Flächen (A. Geisler), Bachelorarbeit Hamburg 2020; PDF 
• Tree-structure in separation systems and infinitary combinatorics (J. Erde), Habilitationsschrift, Hamburg 2019; PDF 
• On Tangles and Trees (D. Weißauer), PhD dissertation, Hamburg 2018; PDF 
• Tangles determined by majority vote (C. Elbracht), MSc dissertation, Hamburg 2017; PDF 
• Abstract tangles as an inverse limit, and a tangle compactification for topological spaces (M. Teegen), MSc dissertation, Hamburg 2017; PDF 
• Infinite tree sets and their representations (J. Kneip), MSc dissertation, Hamburg 2016; PDF
• Characteristics of profiles (Ph. Eberenz), MSc dissertation, Hamburg 2015; PDF