Johannes Carmesin

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
Johannes Carmesin

I am a Reader at University of Birmingham and head of the group in Combinatorics, Probability and Algorithms. My research is funded by EPSRC and I am editor for the journal Discrete Mathematics.

Summer research projects (for students)

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
Click here to see all my papers.

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.


Papers

  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. Entanglements (with J. Kurkofka), Preprint; pdf
  3. A characterisation of 3-colourable 3-dimensional triangulations (with E. Nevinson and B. Saunders), Preprint; pdf
  4. Outerspatial 2-complexes: Extending the class of outerplanar graphs to three dimensions (with T. Mihaylov), Preprint; pdf
  5. A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings, Preprint; pdf
  6. Characterising graphs with no subdivision of a wheel of bounded diameter, Preprint; pdf
  7. Local 2-separators, Preprint; pdf
  8. Large highly connected subgraphs in graphs with linear average degree, Preprint; pdf
  9. New Constructions related to the Polynomial Sphere Recognition Problem (with L. Lichev), Discret. Comput. Geom., volume 67, 2022, pages 1097-1123; pdf
  10. Canonical trees of tree-decompositions (with M. Hamann and B. Miraftab), Journal of Combinatorial Theory, Series B, Volume 152, 2022, Pages 1-26; pdf
  11. The Almost Intersection Property for Pairs of Matroids on Common Groundset (with N. Bowler, S. Ghaderi and J. Wojciechowski), Preprint; pdf
  12. Embedding simply connected 2-complexes in 3-space I, Preprint; pdf
  13. Embedding simply connected 2-complexes in 3-space II, Preprint; pdf
  14. Embedding simply connected 2-complexes in 3-space III, Preprint; pdf
  15. Embedding simply connected 2-complexes in 3-space IV, Preprint; pdf
  16. Embedding simply connected 2-complexes in 3-space V, Preprint; pdf
  17. On tree-decompositions of one-ended graphs (with F. Lehner & R. Möller), Math. Nachrichten, to appear; pdf
  18. A Liouville hyperbolic souvlaki (with B. Federici & A. Georgakopoulos), Electron. J. Probab., Volume 22 (2017), paper no. 36, 19 pages; pdf
  19. The colouring number of infinite graphs (with N. Bowler, P. Komjáth & C. Reiher), Combinatorica, to appear; pdf
  20. A short proof that every finite graph has a tree-decomposition displaying its tangles, European J. Combin. 58 (2016), 61-65; pdf
  21. 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
  22. Reconstruction of infinite matroids from their 3-connected minors (with N. Bowler & L. Postle), European J. Combin. (2018), volume 67, pages 126-144; pdf
  23. Every planar graph with the Liouville property is amenable (with Agelos Georgakopoulos), RSA, to appear; pdf
  24. All graphs have tree-decompositions displaying their topological ends, Combinatorica, Volume 39 (2019), pages 545-596; pdf
  25. Topological cycle matroids of infinite graphs, European J. Combin, Volume 60 (2017), Pages 135-150; pdf
  26. Infinite trees of matroids (with Nathan Bowler), Preprint; pdf
  27. On the intersection conjecture for infinite trees of matroids (with Nathan Bowler), Preprint; pdf
  28. Even an infinite bureaucracy eventually makes a decision, Preprint; pdf
  29. Topological infinite gammoids, and a new Menger-type theorem for infinite graphs, Electron. J. Combin. 25(2018), no. 3, paper 3.38, 22pp; pdf
  30. Infinite graphic matroids Part I (with Nathan Bowler & Robin Christian), Combinatorica (2018), volume 38, issue 2, pages 305-339; pdf
  31. 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
  32. The ubiquity of Psi-matroids (with Nathan Bowler), Preprint; pdf
  33. Infinite Matroids and Determinacy of Games (with Nathan Bowler), Preprint; pdf
  34. 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
  35. 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
  36. 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
  37. An excluded minors method for infinite matroids (with Nathan Bowler), J. Combin. Theory Ser. B (2018), volume 128, pp. 104-113; pdf
  38. Matroid intersection, base packing and base covering for infinite matroids (with Nathan Bowler), Combinatorica 35 (2015), no. 2, 153-180; pdf
  39. Matroids with an infinite circuit-cocircuit intersection (with Nathan Bowler), J. Combin. Theory Ser. B (2014), volume 107, 78-91; pdf
  40. On the intersection of infinite matroids (with Elad Aigner-Horev & Jan-Oliver Fröhlich), Discrete Mathematics (2018), volume 341, issue 6, pages 1582-1596; pdf
  41. Connectivity and tree-structure in finite graphs (with Reinhard Diestel, Fabian Hundertmark & Maya Stein), Combinatorica 34 (2014) , 11-46; pdf
  42. 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)

Dissertation (2015)

Habilitation (2018)


Combinatorics, Probability and Algorithms @ Bham , Combinatorics Seminar