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 member of the group in Combinatorics, Probability and Algorithms. My research is funded by EPSRC and I am editor for the journals Discrete Mathematics and Innovations in Graph Theory.

Birmingham Maths Research Festival (for students)

Selected Papers

  1. Local 2-separators, Journal of Combinatorial Theory, Series B, Volume 156, 2022, Pages 101-144, pdf
  2. Canonical decompositions of 3-connected graphs (with J. Kurkofka), FOCS 2023, 50 pages; pdf
  3. Embedding simply connected 2-complexes in 3-space, pages 91, Preprint; pdf
  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. New approaches include "local separators" of graphs as well as "angry theorems" for 3-connected 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.


My team

Jan Kurkofka (Postdoc)
Emily Nevinson (PhD)
Will Turner (PhD)
Tim Planken (PhD)
Romain Bourneuf (Visitor)

Papers

  1. Embedding simply connected 2-complexes in 3-space, Preprint; pdf
  2. Canonical decompositions of 3-connected graphs (with J.Kurkofka), FOCS 2023, 50 pages; pdf
  3. Characterising 4-tangles through a connectivity property (with J.Kurkofka), Preprint; pdf
  4. 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
  5. Dual matroids of 2-complexes -- revisited, Preprint; pdf
  6. On Andreae's Ubiquity Conjecture, Journal of Combinatorial Theory, Series B 162, pages 68-70 (2023); pdf
  7. Entanglements (with J. Kurkofka), Preprint; pdf
  8. A characterisation of 3-colourable 3-dimensional triangulations (with E. Nevinson and B. Saunders), Preprint; pdf
  9. Outerspatial 2-complexes: Extending the class of outerplanar graphs to three dimensions (with T. Mihaylov), Preprint; pdf
  10. A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings, Preprint; pdf
  11. Characterising graphs with no subdivision of a wheel of bounded diameter, Journal of Combinatorial Theory, Series B, Volume 161, Pages 21-51 (2023); pdf
  12. Local 2-separators, Journal of Combinatorial Theory, Series B, Volume 156, 2022, Pages 101-144, pdf
  13. Large highly connected subgraphs in graphs with linear average degree, Preprint; pdf
  14. New Constructions related to the Polynomial Sphere Recognition Problem (with L. Lichev), Discret. Comput. Geom., volume 67, 2022, pages 1097-1123; pdf
  15. Canonical trees of tree-decompositions (with M. Hamann and B. Miraftab), Journal of Combinatorial Theory, Series B, Volume 152, 2022, Pages 1-26; pdf
  16. The Almost Intersection Property for Pairs of Matroids on Common Groundset (with N. Bowler, S. Ghaderi and J. Wojciechowski), The Electronic Journal of Combinatorics, Pages 3-5 (2020); pdf
  17. Embedding simply connected 2-complexes in 3-space I, Preprint; pdf
  18. Embedding simply connected 2-complexes in 3-space II, Preprint; pdf
  19. Embedding simply connected 2-complexes in 3-space III, Preprint; pdf
  20. Embedding simply connected 2-complexes in 3-space IV, Preprint; pdf
  21. Embedding simply connected 2-complexes in 3-space V, Preprint; pdf
  22. On tree-decompositions of one-ended graphs (with F. Lehner & R. Möller), Math. Nachrichten 292.3: Pages 524-539 (2019); pdf
  23. A Liouville hyperbolic souvlaki (with B. Federici & A. Georgakopoulos), Electron. J. Probab., Volume 22 (2017), paper no. 36, 19 pages; pdf
  24. The colouring number of infinite graphs (with N. Bowler, P. Komjáth & C. Reiher), Combinatorica, Volume 39, Pages 1225-1235 (2019); pdf
  25. A short proof that every finite graph has a tree-decomposition displaying its tangles, European J. Combin. 58 (2016), 61-65; pdf
  26. 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
  27. Reconstruction of infinite matroids from their 3-connected minors (with N. Bowler & L. Postle), European J. Combin. (2018), volume 67, pages 126-144; pdf
  28. Every planar graph with the Liouville property is amenable (with Agelos Georgakopoulos), Random Structures & Algorithms 57.3: Pages 706-729 (2020); pdf
  29. All graphs have tree-decompositions displaying their topological ends, Combinatorica, Volume 39 (2019), pages 545-596; pdf
  30. Topological cycle matroids of infinite graphs, European J. Combin, Volume 60 (2017), Pages 135-150; pdf
  31. Infinite trees of matroids (with Nathan Bowler), Preprint; pdf
  32. On the intersection conjecture for infinite trees of matroids (with Nathan Bowler), Preprint; pdf
  33. Even an infinite bureaucracy eventually makes a decision, Preprint; pdf
  34. Topological infinite gammoids, and a new Menger-type theorem for infinite graphs, Electron. J. Combin. 25(2018), no. 3, paper 3.38, 22pp; pdf
  35. Infinite graphic matroids Part I (with Nathan Bowler & Robin Christian), Combinatorica (2018), volume 38, issue 2, pages 305-339; pdf
  36. 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
  37. The ubiquity of Psi-matroids (with Nathan Bowler), Preprint; pdf
  38. Infinite Matroids and Determinacy of Games (with Nathan Bowler), Preprint; pdf
  39. 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
  40. 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
  41. 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
  42. An excluded minors method for infinite matroids (with Nathan Bowler), J. Combin. Theory Ser. B (2018), volume 128, pp. 104-113; pdf
  43. Matroid intersection, base packing and base covering for infinite matroids (with Nathan Bowler), Combinatorica 35 (2015), no. 2, 153-180; pdf
  44. Matroids with an infinite circuit-cocircuit intersection (with Nathan Bowler), J. Combin. Theory Ser. B (2014), volume 107, 78-91; pdf
  45. On the intersection of infinite matroids (with Elad Aigner-Horev & Jan-Oliver Fröhlich), Discrete Mathematics (2018), volume 341, issue 6, pages 1582-1596; pdf
  46. Connectivity and tree-structure in finite graphs (with Reinhard Diestel, Fabian Hundertmark & Maya Stein), Combinatorica 34 (2014) , 11-46; pdf
  47. 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