Tung H. Nguyen
Email: nguyent [at] maths.ox.ac.uk; tunghn [at] math.princeton.edu
Office: Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
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
Ramsey properties of hereditary graph classes
- Induced subgraph density. VII. The five-vertex path
(with A. Scott and P. Seymour),
Proc. Lond. Math. Soc. (3) 132 (2026), no. 3, Paper No. e70133, 21 pp.
- Induced subgraph density. VI. Bounded VC-dimension
(with A. Scott and P. Seymour),
Adv. Math. 482 (2025), part A, Paper No. 110601, 20 pp.
- Induced subgraph density. V. All paths approach Erdős–Hajnal
(with A. Scott and P. Seymour),
Adv. Comb., accepted.
- Induced subgraph density. IV. New graphs with the Erdős–Hajnal property
(with A. Scott and P. Seymour),
Trans. Amer. Math. Soc., accepted.
- Induced subgraph density. III. Cycles and subdivisions
(with A. Scott and P. Seymour),
preprint.
- Induced subgraph density. II. Sparse and dense sets in cographs
(with J. Fox, A. Scott, and P. Seymour),
European J. Combin. 124 (2025), Paper No. 104075, 14 pp.
- Induced subgraph density. I. A $\text{loglog}$ step towards Erdős–Hajnal
(with M. Bucić, A. Scott, and P. Seymour),
Int. Math. Res. Not. IMRN 12 (2024), 9991–10004.
- Trees and near-linear stable sets
(with A. Scott and P. Seymour),
Combinatorica 45 (2025), no. 4, Paper No. 49, 18 pp.
- Subdivisions and near-linear stable sets
(with A. Scott and P. Seymour),
Combinatorica 45 (2025), no. 4, Paper No. 39, 12 pp.
- Fractionally colouring $P_5$-free graphs,
unpublished.
$\chi$-boundedness
- Polynomial $\chi$-boundedness for excluding $P_5$,
preprint. Preliminary version accepted to FOCS 2026.
- Ramsey-type $\chi$-bounds for $\chi$-bounded graph classes
(with S. Oum),
preprint.
- Polynomial bounds for chromatic number. VIII. Excluding a path and a complete multipartite graph
(with A. Scott and P. Seymour),
J. Graph Theory 107 (2024), 509–521.
- A note on the Gyárfás–Sumner conjecture
(with A. Scott and P. Seymour),
Graphs Combin. 40 (2024), no. 2, Paper No. 33, 6 pp.
- On a problem of El-Zahar and Erdős
(with A. Scott and P. Seymour),
J. Combin. Theory Ser. B 165 (2024), 211–222.
- On polynomially high-chromatic pure pairs,
unpublished.
Coarse graph theory
- Asymptotic structure. VI. Distant paths across a disc
(with A. Scott and P. Seymour),
preprint.
- Asymptotic structure. V. The coarse Menger conjecture in bounded path-width
(with A. Divoux, A. Scott, and P. Seymour),
preprint.
- Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture
(with A. Scott and P. Seymour),
preprint.
- Asymptotic structure. III. Excluding a fat tree
(with A. Scott and P. Seymour),
preprint.
- Asymptotic structure. II. Path-width and additive quasi-isometry
(with A. Scott and P. Seymour),
preprint.
- Asymptotic structure. I. Coarse tree-width
(with A. Scott and P. Seymour),
preprint.
- A counterexample to the coarse Menger conjecture
(with A. Scott and P. Seymour),
J. Combin. Theory Ser. B 173 (2025), 68–82.
Connectivity and graph minors
- Graphs without a 3-connected subgraph are 4-colourable
(with E. Bonnet, C. Feghali, A. Scott, P. Seymour, S. Thomassé, and N. Trotignon),
Electron. J. Combin. 32 (2025), no. 1, Paper No. 1.26, 11pp.
- Highly connected subgraphs with large chromatic number,
SIAM J. Discrete Math. 38 (2024), no. 1, 243–260.
- The average cut-rank of graphs
(with Sang-il Oum),
European J. Combin. 90 (2020), Paper No. 103183, 22 pp.
- Linear-sized minors with given edge density,
unpublished.
Digraphs and tournaments
Other topics
- The vertex sets of subtrees of a tree
(with M. Chudnovsky, A. Scott, and P. Seymour),
Electron. J. Combin. 33 (2026), no. 2, Paper No. 2.7, 10 pp.
- Clique covers of $H$-free graphs
(with A. Scott, P. Seymour, and S. Thomassé),
European J. Combin. 118 (2024), Paper No. 103909, 10 pp.
- Induced paths in graphs without anticomplete cycles
(with A. Scott and P. Seymour),
J. Combin. Theory Ser. B 164 (2024), 321–339.
- A further extension of Rödl's theorem,
Electron. J. Combin. 30 (2023), no. 3, Paper No. 3.22, 16 pp.
- Growing balanced covering sets,
Discrete Math. 344 (2021), no. 11, Paper No. 112554, 6 pp.
Google Scholar
ORCID
arXiv