Tung H. Nguyen

Email: nguyent [at] maths.ox.ac.uk, tunghn [at] math.princeton.edu
Address: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG

Hello! I am currently working at the University of Oxford as a Titchmarsh Research Fellow at the Mathematical Institute and a Postdoctoral Research Fellow at Christ Church.

I obtained a PhD in Applied and Computational Mathematics from Princeton University where I was supervised by Paul Seymour and was a Jacobus Fellow in the final year. Before Princeton, I earned a Bachelor of Science in Mathematical Sciences from KAIST, working with Sang-il Oum.

My Vietnamese name is Nguyễn Huy Tùng.

I am interested in discrete mathematics, mostly structural and extremal problems in graph theory.

I have maintained the lists of problems submitted to two Barbados graph theory workshops: 2022a and 2024.

Some notes on recent work on the Erdős–Hajnal conjecture.

PhD thesis: Induced Subgraph Density.

Papers

Preprints

  1. Fractionally colouring $P_5$-free graphs, preprint.
  2. Line-width and path-width (with A. Scott and P. Seymour), preprint.
  3. Asymptotic structure. VI. Distant paths across a disc (with A. Scott and P. Seymour), preprint.
  4. Asymptotic structure. V. The coarse Menger conjecture in bounded path-width (with A. Scott and P. Seymour), preprint.
  5. Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture (with A. Scott and P. Seymour), preprint.
  6. Asymptotic structure. III. Excluding a fat tree (with A. Scott and P. Seymour), preprint.
  7. Asymptotic structure. II. Path-width and additive quasi-isometry (with A. Scott and P. Seymour), preprint.
  8. Asymptotic structure. I. Coarse tree-width (with A. Scott and P. Seymour), preprint.
  9. The vertex sets of subtrees of a tree (with M. Chudnovsky, A. Scott, and P. Seymour), preprint.
  10. On polynomially high-chromatic pure pairs, preprint.
  11. Distant digraph domination (with A. Scott and P. Seymour), preprint.
  12. Induced subgraph density. VII. The five-vertex path (with A. Scott and P. Seymour), preprint.
  13. Induced subgraph density. V. All paths approach Erdős–Hajnal (with A. Scott and P. Seymour), preprint.
  14. Induced subgraph density. IV. New graphs with the Erdős–Hajnal property (with A. Scott and P. Seymour), preprint.
  15. Induced subgraph density. III. Cycles and subdivisions (with A. Scott and P. Seymour), preprint.
  16. Linear-sized minors with given edge density, preprint.

Accepted/Published

  1. Induced subgraph density. VI. Bounded VC-dimension (with A. Scott and P. Seymour), Advances in Mathematics, accepted.
  2. Trees and near-linear stable sets (with A. Scott and P. Seymour), Combinatorica 45 (2025), no. 5, Paper No. 49.
  3. Subdivisions and near-linear stable sets (with A. Scott and P. Seymour), Combinatorica 45 (2025), no. 4, Paper No. 39.
  4. Graphs without a 3-connected subgraph are 4-colourable (with E. Bonnet, C. Feghali, A. Scott, P. Seymour, S. Thomassé, and N. Trotignon), Electronic Journal of Combinatorics 32 (2025), no. 1, Paper No. 1.26, 11pp.
  5. Some results and problems on tournament structure (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 173 (2025), 146–183.
  6. A counterexample to the coarse Menger conjecture (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 173 (2025), 68–82.
  7. Induced subgraph density. II. Sparse and dense sets in cographs (with J. Fox, A. Scott, and P. Seymour), European Journal of Combinatorics 124 (2025), Paper No. 104075.
  8. Polynomial bounds for chromatic number. VIII. Excluding a path and a complete multipartite graph (with A. Scott and P. Seymour), Journal of Graph Theory 107 (2024), 509–521.
  9. Induced subgraph density. I. A $\text{loglog}$ step towards Erdős–Hajnal (with M. Bucić, A. Scott, and P. Seymour), International Mathematics Research Notices 12 (2024), 9991–10004.
  10. A note on the Gyárfás–Sumner conjecture (with A. Scott and P. Seymour), Graphs and Combinatorics 40 (2024), no. 2, Paper No. 33, 6pp.
  11. Highly connected subgraphs with large chromatic number, SIAM Journal on Discrete Mathematics 38 (2024), no. 1, 243–260.
  12. Clique covers of $H$-free graphs (with A. Scott, P. Seymour, and S. Thomassé), European Journal of Combinatorics 118 (2024), Paper No. 103909, 10 pp.
  13. On a problem of El-Zahar and Erdős (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 165 (2024), 211–222.
  14. Induced paths in graphs without anticomplete cycles (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 164 (2024), 321–339.
  15. A further extension of Rödl's theorem, Electronic Journal of Combinatorics 30 (2023), no. 3, Paper No. 3.22, 16pp.
  16. Growing balanced covering sets, Discrete Mathematics 344 (2021), no. 11, Paper No. 112554, 6pp.
  17. The average cut-rank of graphs (with S. Oum), European Journal of Combinatorics 90 (2020), Paper No. 103183, 22 pp.

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