Dr Johannes Carmesin School of Mathematics University of Birmingham Edgbaston, Birmingham B15 2TT, UK

Room 204, Watson Building E-Mail: J.Carmesin@bham.ac.uk

Selected Papers

1. Local 2-separators, Preprint; pdf
2. A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings, Preprint; pdf
3. Embedding simply connected 2-complexes in 3-space I, II, III, IV, V
4. All graphs have tree-decompositions displaying their topological ends, Combinatorica, Volume 39 (2019), pages 545-596; pdf
5. Graph Theory - A Survey on the Occasion of the Abel Prize for László Lovász, Jahresbericht der Deutschen Mathematiker-Vereinigung volume 124, pages 83-108 (2022); pdf

My research interests include:

	Combinatorics in 3 dimensions A key goal here is to extend the fundamental methods from Structural Graph Theory to study 2-dimensional simplicial complexes. The starting point for this project is my 3-dimensional analogue of Kuratowski's theorem.
	Graph Minors and Connectivity A minor of a graph is obtained by deleting and contracting edges. The connection of Graph Minor Theory with topology is already apparent from this definition as deletions and contractions are "dual operations" for plane graphs, and even more so in the Graph Minor Structure Theorem of Robertson and Seymour . Here I am particularly interested in studying connectivity and tree-decompositions, and using its methods in other areas. A new approach are "local separators" of graphs.
	Matroids A fundamental theorem in Matroid Theory is Whitney's characterisation of graph planarity in terms of matroids. I extended this theorem to 3-dimensional space. Another direction of research is to extend Whitney's theorem to surfaces, which led to a characterisation of graphs admitting locally planar embeddings.
	Infinite Graphs An important tool to study infinite graphs are ends, which can be seen as boundary points at infinity of the graph. In my PhD, I proved Halin's end-faithful spanning-tree conjecture in amended form.

1. Graph Theory - A Survey on the Occasion of the Abel Prize for László Lovász, Jahresbericht der Deutschen Mathematiker-Vereinigung volume 124, pages 83-108 (2022); pdf
2. Dual matroids of 2-complexes -- revisited, Preprint; pdf
3. On Andreae's Ubiquity Conjecture, Preprint; pdf
4. Entanglements (with J. Kurkofka), Preprint; pdf
5. A characterisation of 3-colourable 3-dimensional triangulations (with E. Nevinson and B. Saunders), Preprint; pdf
6. Outerspatial 2-complexes: Extending the class of outerplanar graphs to three dimensions (with T. Mihaylov), Preprint; pdf
7. A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings, Preprint; pdf
8. Characterising graphs with no subdivision of a wheel of bounded diameter, Preprint; pdf
9. Local 2-separators, Preprint; pdf
10. Large highly connected subgraphs in graphs with linear average degree, Preprint; pdf
11. New Constructions related to the Polynomial Sphere Recognition Problem (with L. Lichev), Discret. Comput. Geom., volume 67, 2022, pages 1097-1123; pdf
12. Canonical trees of tree-decompositions (with M. Hamann and B. Miraftab), Journal of Combinatorial Theory, Series B, Volume 152, 2022, Pages 1-26; pdf
13. The Almost Intersection Property for Pairs of Matroids on Common Groundset (with N. Bowler, S. Ghaderi and J. Wojciechowski), Preprint; pdf
14. Embedding simply connected 2-complexes in 3-space I, Preprint; pdf
15. Embedding simply connected 2-complexes in 3-space II, Preprint; pdf
16. Embedding simply connected 2-complexes in 3-space III, Preprint; pdf
17. Embedding simply connected 2-complexes in 3-space IV, Preprint; pdf
18. Embedding simply connected 2-complexes in 3-space V, Preprint; pdf
19. On tree-decompositions of one-ended graphs (with F. Lehner & R. Möller), Math. Nachrichten, to appear; pdf
20. A Liouville hyperbolic souvlaki (with B. Federici & A. Georgakopoulos), Electron. J. Probab., Volume 22 (2017), paper no. 36, 19 pages; pdf
21. The colouring number of infinite graphs (with N. Bowler, P. Komjáth & C. Reiher), Combinatorica, to appear; pdf
22. A short proof that every finite graph has a tree-decomposition displaying its tangles, European J. Combin. 58 (2016), 61-65; pdf
23. Canonical tree-decompositions of a graph that display its k-blocks (with Pascal Gollin), J. Combin. Theory Ser. B , Volume 122 (2017), Pages 1-20; pdf
24. Reconstruction of infinite matroids from their 3-connected minors (with N. Bowler & L. Postle), European J. Combin. (2018), volume 67, pages 126-144; pdf
    
25. Every planar graph with the Liouville property is amenable (with Agelos Georgakopoulos), RSA, to appear; pdf
26. All graphs have tree-decompositions displaying their topological ends, Combinatorica, Volume 39 (2019), pages 545-596; pdf
27. Topological cycle matroids of infinite graphs, European J. Combin, Volume 60 (2017), Pages 135-150; pdf
    
28. Infinite trees of matroids (with Nathan Bowler), Preprint; pdf
29. On the intersection conjecture for infinite trees of matroids (with Nathan Bowler), Preprint; pdf
30. Even an infinite bureaucracy eventually makes a decision, Preprint; pdf
31. Topological infinite gammoids, and a new Menger-type theorem for infinite graphs, Electron. J. Combin. 25(2018), no. 3, paper 3.38, 22pp; pdf
32. Infinite graphic matroids Part I (with Nathan Bowler & Robin Christian), Combinatorica (2018), volume 38, issue 2, pages 305-339; pdf
33. Edge-disjoint double rays in infinite graphs: a Halin type result (with Nathan Bowler & Julian Pott), J. Combin. Theory Ser. B 111 (2015), 1-16; pdf
34. The ubiquity of Psi-matroids (with Nathan Bowler), Preprint; pdf
35. Infinite Matroids and Determinacy of Games (with Nathan Bowler), Preprint; pdf
36. Canonical tree-decompositions of finite graphs II. Essential parts (with R. Diestel, M. Hamann & F. Hundertmark), J. Combin. Theory Ser. B 118 (2016), 268-283; pdf
37. Canonical tree-decompositions of finite graphs I. Existence and algorithms (with R. Diestel, M. Hamann & F. Hundertmark), J. Combin. Theory Ser. B 116 (2016), 1-24; pdf
38. k-Blocks: a connectivity invariant for graphs (with R. Diestel, M. Hamann & F. Hundertmark), SIAM J. Discrete Math. , 28-4 (2014), pp. 1876-1891; pdf
39. An excluded minors method for infinite matroids (with Nathan Bowler), J. Combin. Theory Ser. B (2018), volume 128, pp. 104-113; pdf
40. Matroid intersection, base packing and base covering for infinite matroids (with Nathan Bowler), Combinatorica 35 (2015), no. 2, 153-180; pdf
41. Matroids with an infinite circuit-cocircuit intersection (with Nathan Bowler), J. Combin. Theory Ser. B (2014), volume 107, 78-91; pdf
42. On the intersection of infinite matroids (with Elad Aigner-Horev & Jan-Oliver Fröhlich), Discrete Mathematics (2018), volume 341, issue 6, pages 1582-1596; pdf
43. Connectivity and tree-structure in finite graphs (with Reinhard Diestel, Fabian Hundertmark & Maya Stein), Combinatorica 34 (2014) , 11-46; pdf
44. A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy, Potential Analysis 37 (2012), 229-245; pdf

Master thesis (2012)

• A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy; pdf

Dissertation (2015)

• Tree-decompositions in finite and infinite graphs; pdf

Habilitation (2018)

• Embedding simply connected 2-complexes in 3-space, and further results on infinite graphs and matroids; pdf