Joshua Erde - Main  |  About me  |  Research  |  Publications  |  Teaching  |  Institute

Preprints

  • (With M. Collares, A. Geisler and M. Kang) Counting independent sets in expanding bipartite regular graphs, submitted (arXiv).

  • (With M. Anastos, M. Kang and V. Pfenninger) The law of the circumference of sparse binomial random graphs, submitted (arXiv).

  • (With S. Diskin, M. Kang and M. Krivelevich) Large matchings and nearly spanning, nearly regular subgraphs of random subgraphs, submitted (arXiv).

  • (With M. Collares, A. Geisler and M. Kang) Universal behaviour of majority bootstrap percolation on high-dimensional geometric graphs, submitted (arXiv).

  • (With M. Collares and J. Doolittle) The evolution of the permutahedron, submitted (arXiv).

  • Matchings in the hypercube with specified edges, submitted (arXiv).

Journal Articles

    Accepted

  1. (With S. Diskin, M. Kang and M. Krivelevich) Percolation through isoperimetry, Annales de l'Institut Henri Poincaré, to appear (Journal/arXiv).

  2. (With F. Lehner, M. Kang, D. Schmid and B. Mohar) Catching a robber on a random k-uniform hypergraph, Canadian Journal of Mathematics, to appear (Journal/arXiv).

    3. 2025

  3. (With O. Cooley, T. Do and M. Missethan) The emergence of a giant rainbow component, European Journal of Combinatorics, Volume 127, 2025 (Journal/arXiv).

  4. (With M. Collares S. Diskin and M. Krivelevich) Long cycles in percolated expanders, Electronic Journal of Combinatorics, Volume 32, Issue 1, 2025 (Journal/arXiv).

  5. (With S. Diskin, M. Kang and M. Krivelevich) Percolation on high-dimensional product graphs, Random Structures and Algorithms, Volume 66, Issue 1, 2025 (Journal/arXiv).

    6. 2024

  6. (With N. Bowler, C. Elbracht, J. P. Gollin, K. Heuer, M. Pitz and M. Teegen) Ubiquity of locally finite graphs with extensive tree-decompositions, Combinatorial Theory, Volume 4, Issue 2, 2024 (Journal/arXiv).

  7. (With S. Diskin, M. Kang and M. Krivelevich) Isoperimetric inequalities and supercritical percolation on high-dimensional product graphs, Combinatorica, Volume 44, 2024 (Journal/arXiv).

  8. (With T. Do and M. Kang) A note on the width of sparse random graphs, Journal of Graph Theory, Volume 106, Issue 2, 2024 (Journal/arXiv).

  9. (With R. Diestel, C. Elbracht and M. Teegen) Duality and tangles of set separations, Journal of Combinatorics, Volume 15, Issue 1, 2024 (Journal/arXiv).

  10. (With S. Diskin, M. Kang and M. Krivelevich) Percolation on irregular high-dimensional product graphs, Combinatorics, Probability and Computing, volume 33, Issue 3, 2024 (Journal/arXiv).

    11. 2023

  11. (With T. Do, M. Kang and M. Missethan) Component behaviour and excess of random bipartite graphs near the critical point, Electronic Journal of Combinatorics, Volume 30, Issue 3, 2023 (Journal/arXiv).

  12. (With B. Barber, P. Keevash and A. Roberts) Isoperimetric stability in lattices, Proceedings of the American Mathematical Society, Volume 151, 2023 (Journal/arXiv).

  13. (With N. Bowler, C. Elbracht, J. P. Gollin, K. Heuer, M. Pitz and M. Teegen) Ubiquity of graphs with non-linear end structure, Journal of Graph Theory, Volume 103, Issue 3, 2023 (Journal/arXiv).

  14. (With M. Kang and M. Krivelevich) Expansion in supercritical random subgraphs of the hypercube and its consequences, Annals of Probability, Volume 51, Issue 1, 2023 (Journal/arXiv).

    15. 2022

  15. (With F. Lehner) Hamiltonian decompositions of 4-regular Cayley graphs of infinite abelian groups, Journal of Graph Theory, Volume 101, Issue 3, 2022 (Journal/arXiv).

  16. (With T. Do and M. Kang) Planarity and genus of sparse random bipartite graphs, SIAM Journal on Discrete Mathematics, Volume 36, Issue 2, 2022 (Journal/(arXiv).

  17. (With N. Bowler, C. Elbracht, J. P. Gollin, K. Heuer, M. Pitz and M. Teegen) Topological ubiquity of trees, Journal of Combinatorial Theory, Series B, Volume 157, 2022 (Journal/arXiv).

    18. 2021

  18. (With N. Bowler, F. Lehner and M. Pitz) Bounding the cop number of a graph by its genus, SIAM Journal on Discrete Mathematics, Volume 35, Issue 4, 2021 (Journal/arXiv).

  19. (With J. P. Gollin and A. Joó) Enlarging vertex-flames in countable digraphs, Journal of Combinatorial Theory, Series B, Volume 151, 2021 (Journal/arXiv).

  20. (With J. P. Gollin, A. Joó, P. Knappe and M. Pitz) Base partition for finitary-cofinitary matroid families, Combinatorica, Volume 41, 2021 (Journal/arXiv).

  21. (With J. P. Gollin, A. Joó, P. Knappe and M. Pitz) A Cantor-Bernstein-type theorem for spanning trees in infinite graphs, Journal of Combinatorial Theory, Series B, Volume 149, 2021 (Journal/arXiv).

    22. 2020

  22. (With M. Kang and M. Krivelevich) Large complete minors in random subgraphs, Combinatorics, Probability and Computing, Volume 30, Issue 4, 2021 (Journal/arXiv).

  23. Directed path-decompositions, SIAM Journal on Discrete Mathematics, Volume 34, Issue 1, 2020 (Journal/arXiv).

  24. (with F. Lehner and M. Pitz) Hamilton decompositions of one-ended Cayley graphs, Journal of Combinatorial Theory, Series B, Volume 140, 2020 (Journal/arXiv).

    25. 2019

  25. (With D. Weissauer) A short derivation of the structure theorem for graphs with excluded topological minors, SIAM Journal on Discrete Mathematics, Volume 33, Issue 3, 2019 (Journal/arXiv).

  26. (With R. Diestel and D. Weissauer) Structural submodularity and tangles in abstract separation systems, Journal of Combinatorial Theory, Series A, Volume 167, 2019 (Journal/arXiv).

    27. 2018

  27. (with N. Bowler, P. Heinig, F. Lehner and M. Pitz) Non-reconstructible locally finite graphs, Journal of Combinatorial Theory, Series B, Volume 133, 2018 (Journal/arXiv).

  28. (with B. Barber) Isoperimetry in integer lattices, Discrete Analysis, Volume 7, 2018 (Journal/arXiv).

  29. A unified treatment of linked and lean tree-decompositions, Journal of Combinatorial Theory, Series B, Volume 130, 2018 (Journal/arXiv).

    30. 2017

  30. (with N. Bowler, F. Lehner, M. Merker, M. Pitz and K. Stavropoulos) A counterexample to Montgomery's conjecture on dynamic colourings of regular graphs, Discrete Applied Mathematics, Volume 229, 2017 (Journal/arXiv).

  31. (with N. Bowler, P. Heinig, F. Lehner and M. Pitz) A counterexample to the reconstruction conjecture for locally finite trees, The Bulletin of the London Mathematical Society, Volume 49, Issue 4, 2017 (Journal/arXiv).

  32. (with R. Diestel and P. Eberenz) Duality theorems for tangles in graphs, SIAM Journal on Discrete Mathematics, Volume 31, Issue 3, 2017 (Journal/arXiv).

  33. Refining a tree-decomposition which distinguishes tangles, SIAM Journal on Discrete Mathematics, Volume 31, Issue 3, 2017 (Journal/arXiv).

    34. 2016

  34. (with M. Walters) An n-in-a-row type game, The Electronic Journal of Combinatorics, Volume 23, Issue 3, 2016 (Journal/arXiv).

    35. 2015

  35. An n-in-a-row game, Integers, Volume 15, 2015 (Journal/arXiv).

    36. 2014

  36. A note on the combinatorial derivation of non-small sets, New York Journal of Mathematics, Volume 20, 2014 (Journal/arXiv).

  37. Decomposing the cube into paths, Discrete Mathematics, Volume 336, 2014 (Journal/arXiv).

    38. 2012

  38. (with B. Golénia and S. Golénia) The closed knight tour problem in higher dimensions, The Electronic Journal of Combinatorics, Volume 19, Issue 4, 2012 (Journal/arXiv).

Theses


last modified 1 Feb 2024