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

• Fractionally colouring $P_5$-free graphs, preprint.
• Line-width and path-width (with A. Scott and P. Seymour), preprint.
• 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. 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.
• The vertex sets of subtrees of a tree (with M. Chudnovsky, A. Scott, and P. Seymour), preprint.
• On polynomially high-chromatic pure pairs, preprint.
• Distant digraph domination (with A. Scott and P. Seymour), preprint.
• Induced subgraph density. VII. The five-vertex path (with A. Scott and P. Seymour), preprint.
• Induced subgraph density. V. All paths approach Erdős–Hajnal (with A. Scott and P. Seymour), preprint.
• Induced subgraph density. IV. New graphs with the Erdős–Hajnal property (with A. Scott and P. Seymour), preprint.
• Induced subgraph density. III. Cycles and subdivisions (with A. Scott and P. Seymour), preprint.
• Linear-sized minors with given edge density, preprint.

Accepted/Published

• Induced subgraph density. VI. Bounded VC-dimension (with A. Scott and P. Seymour), Advances in Mathematics 482 (2025), part A, Paper No. 110601.
• Trees and near-linear stable sets (with A. Scott and P. Seymour), Combinatorica 45 (2025), no. 5, Paper No. 49.
• Subdivisions and near-linear stable sets (with A. Scott and P. Seymour), Combinatorica 45 (2025), no. 4, Paper No. 39.
• 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.
• Some results and problems on tournament structure (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 173 (2025), 146–183.
• A counterexample to the coarse Menger conjecture (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 173 (2025), 68–82.
• 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.
• 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.
• 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.
• A note on the Gyárfás–Sumner conjecture (with A. Scott and P. Seymour), Graphs and Combinatorics 40 (2024), no. 2, Paper No. 33, 6pp.
• Highly connected subgraphs with large chromatic number, SIAM Journal on Discrete Mathematics 38 (2024), no. 1, 243–260.
• 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.
• On a problem of El-Zahar and Erdős (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 165 (2024), 211–222.
• Induced paths in graphs without anticomplete cycles (with A. Scott and P. Seymour), Journal of Combinatorial Theory, Series B 164 (2024), 321–339.
• A further extension of Rödl's theorem, Electronic Journal of Combinatorics 30 (2023), no. 3, Paper No. 3.22, 16pp.
• Growing balanced covering sets, Discrete Mathematics 344 (2021), no. 11, Paper No. 112554, 6pp.
• The average cut-rank of graphs (with S. Oum), European Journal of Combinatorics 90 (2020), Paper No. 103183, 22 pp.

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