Richard Montgomery
Papers and preprints Teaching CV
  1. Asymptotically-tight packing and covering with transversal bases in Rota's basis conjecture
    With Lisa Sauermann

  2. Packing subdivisions into regular graphs
    With Kalina Petrova, Arjun Ranganathan and Jane Tan

  3. Almost every Latin square has a decomposition into transversals
    With Candida Bowtell

  4. Almost-full transversals in equi-n-squares
    With Debsoumya Chakraborti, Micha Christoph, Zach Hunter and Teo Petrov

  5. On decomposition thresholds for odd-length cycles and other tripartite graphs
    With Darryn Bryant, Peter Dukes, Daniel Horsley and Barbara Maenhaut

  6. Regular subgraphs at every density
    With Debsoumya Chakraborti, Oliver Janzer and Abhishek Methuku

  7. Approximate path decompositions of regular graphs
    With Alp Müyesser, Alexey Pokrovskiy and Benny Sudakov
    Journal of the London Mathematical Society, to appear

  8. Edge-disjoint cycles with the same vertex set
    With Debsoumya Chakraborti, Oliver Janzer and Abhishek Methuku
    Advances in Mathematics, 2025

  9. Packing the largest trees in the tree packing conjecture
    With Barnabás Janzer

  10. Hamiltonicity of expanders: optimal bounds and applications
    With Nemanja Draganić, David Munhá Correia, Alexey Pokrovskiy and Benny Sudakov

  11. Global rigidity of random graphs in R
    With Rajko Nenadov, Julien Portier and Tibor Szabó

  12. Ramsey numbers of bounded degree trees versus general graphs
    With Jun Yan and Matías Pavez-Signé
    Journal of Combinatorial Theory, Series B, 2025

  13. A proof of the Ryser-Brualdi-Stein conjecture for large even n

  14. Counting spanning subgraphs in dense hypergraphs
    With Matías Pavez-Signé
    Combinatorics, Probability and Computing, 2024

  15. Towards the Erdős-Gallai Cycle Decomposition Conjecture
    With Matija Bucić
    Advances in Mathematics, 2024 (and STOC, 2023)

  16. Trees with many leaves in tournaments
    With Alistair Benford
    Journal of Combinatorial Theory, Series B, 2025

  17. Transversal factors and spanning trees
    With Alp Müyesser and Yani Pehova
    Advances in Combinatorics, 2022

  18. Trees with few leaves in tournaments
    With Alistair Benford
    Journal of Combinatorial Theory, Series B, 2022

  19. Spanning cycles in random directed graphs
    Random Structures & Algorithms, 2024

  20. Spanning trees in dense directed graphs
    With Amarja Kathapurkar
    Journal of Combinatorial Theory, Series B, 2022

  21. A solution to Erdős and Hajnal's odd cycle problem
    With Hong Liu
    Journal of the American Mathematical Society, 2023.

  22. C4-free subgraphs with large average degree
    With Alexey Pokrovskiy and Benny Sudakov
    Israel Journal of Mathematics, 2021.

  23. A proof of Ringel's Conjecture
    With Alexey Pokrovskiy and Benny Sudakov
    Geometric and Functional Analysis, 2021

  24. Decompositions into isomorphic rainbow spanning trees
    With Stefan Glock, Daniela Kühn, and Deryk Osthus
    Journal of Combinatorial Theory, Series B, 2021

  25. Hamiltonicity in random directed graphs is born resilient
    Combinatorics, Probability and Computing, 2020

  26. Minimalist designs
    With Ben Barber, Stefan Glock, Daniela Kühn, Allan Lo and Deryk Osthus
    Random Structures and Algorithms, 2020

  27. Spanning surfaces in 3-graphs
    With Agelos Georgakopoulos, John Haslegrave and Bhargav Narayanan
    Journal of the European Mathematical Society, 2021

  28. Decompositions into spanning rainbow structures
    With Alexey Pokrovskiy and Benny Sudakov
    Proceedings of the London Mathematical Society, 2019

  29. Embedding rainbow trees with applications to graph labelling and decomposition
    With Alexey Pokrovskiy and Benny Sudakov
    Journal of the European Mathematical Society, 2020

  30. Universality for bounded degree spanning trees in randomly perturbed graphs
    With Julia Böttcher, Jie Han, Yoshiharu Kohayakawa, Olaf Parczyk and Yury Person
    Random Structures and Algorithms, 2019

  31. Embedding spanning bounded degree graphs in randomly perturbed graphs
    With Julia Böttcher, Olaf Parczyk and Yury Person
    Mathematika, 2020

  32. Forcing large tight components in 3-graphs
    With Agelos Georgakopoulos and John Haslegrave
    European Journal of Combinatorics, 2019

  33. Fractional clique decompositions of dense graphs
    Random Structures and Algorithms, 2018

  34. Rainbow spanning trees in properly coloured complete graphs
    With Jósef Balogh and Hong Liu
    Discrete Applied Mathematics, 2018

  35. Hamiltonicity in random graphs is born resilient
    Journal of Combinatorial Theory, Series B, 2019

  36. Spanning trees in random graphs
    Advances in Mathematics, 2019

  37. On the decomposition threshold of a given graph
    With Stefan Glock, Daniela Kühn, Allan Lo and Deryk Osthus
    Journal of Combinatorial Theory, Series B, 2019

  38. Fractional clique decompositions of dense graphs and hypergraphs
    With Ben Barber, Daniela Kühn, Allan Lo and Deryk Osthus
    Journal of Combinatorial Theory, Series B, 2017

  39. Fractional clique decompositions of partite graphs
    Combinatorics, Probability and Computing, 2017

  40. A proof of Mader's conjecture on large clique subdivisions in C_4-free graphs
    With Hong Liu
    Journal of the London Mathematical Society, 2017

  41. Almost all friendly matrices have many obstructions
    SIAM Journal on Discrete Mathematics, 2015

  42. Logarithmically-small minors and topological minors
    Journal of the London Mathematical Society, 2015

    Surveys and expository articles

  1. Cycles and expansion in graphs
    European Mathematics Society magazine, to appear

  2. Recent progress in the study of Latin squares
    Proceedings of the 9th European Congress of Mathematics, to appear

  3. Latin squares via Graph Theory
    London Mathematical Society Newsletter, May 2025

  4. Transversals in Latin squares
    Surveys in Combinatorics, 2024