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Thresholds for Latin squares and Steiner triple systems: Bounds within a logarithmic factor,
with D. Kang, D. Kühn, A. Methuku, and D. Osthus.
Submitted, 26 pages. arXiv:2206.14472.
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Solution to a problem of Erdős on the chromatic index of hypergraphs with bounded codegree,
with D. Kang, D. Kühn, A. Methuku, and D. Osthus.
Submitted, 23 pages. arXiv:2110.06181.
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A special case of Vu's conjecture: Coloring nearly disjoint graphs of bounded maximum degree
with D. Kühn and D. Osthus.
Submitted, 13 pages. arXiv:2109.11438.
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A proof of the Erdős-Faber-Lovász conjecture,
with D. Kang, D. Kühn, A. Methuku, and D. Osthus.
Submitted, 39 pages. arXiv:2101.04698.
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Fractional vertex-arboricity of planar graphs,
with M. Bonamy, F. Kardos, and L. Postle.
Submitted, 14 pages. arXiv:2009.12189.
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Fractional coloring with local demands,
with L. Postle.
Split into three forthcoming papers, 37 pages. arXiv:1811.11806.
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Graph and hypergraph colouring via nibble methods: A survey,
with D. Kang, D. Kühn, A. Methuku, and D. Osthus.
To appear in the proceedings of the 8th European Congress of Mathematics. arXiv:2106.13733.
Bounding χ by a fraction of Δ for graphs without large cliques,
with M. Bonamy, P. Nelson, and L. Postle.
To appear in Journal of Combinatorial Theory, Series B., 14 pages. arXiv:1803.01051.
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On the density of critical graphs with no large cliques,
with L. Postle.
To appear in Combinatorica, 26 pages. arXiv:1911.02661.
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Hamilton transversals in random Latin squares,
with S. Gould.
Random Structures & Algorithms. (Advance online publication).
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Almost all optimally coloured complete graphs contain a rainbow Hamilton path,
with S. Gould, D. Kühn, and D. Osthus.
Journal of Combinatorial Theory, Series B.,
156:57-100, 2022.
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Colourings, transversals and local sparsity,
with R. J. Kang.
Random Structures & Algorithms.,
61(1):173-192, 2022.
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A local epsilon version of Reed's Conjecture,
with L. Postle.
Journal of Combinatorial Theory, Series B.,
141:181-222, 2020.
(Extended abstract in Eurocomb '17)
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The structure of binary matroids with no induced claw or Fano plane restriction,
with M. Bonamy, F. Kardos, P. Nelson, and L. Postle.
Advances in Combinatorics, 2019:1, 17pp.
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Size of the largest induced forest in subcubic graphs of girth at least four and five,
with C.-H. Liu.
Journal of Graph Theory, 89(4):457-478, 2018.
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Induced 2-degenerate subgraphs of triangle-free planar graphs,
with Z. Dvořák.
Electronic Journal of Combinatorics, 25(1):#P1.62, 18, 2018.
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Exponentially many 4-list-colorings of triangle-free graphs on surfaces,
with L. Postle.
Journal of Graph Theory, 87(2):230-238, 2018.
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Minimum size of feedback vertex sets of planar graphs of girth at least five,
with C.-H. Liu.
European Journal of Combinatorics, 61C:138-150, 2017.
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Bounds on the maximum number of minimum dominating sets,
with S. Connolly, Z. Gabor, A. Godbole, and B. Kay.
Discrete Mathematics, 339(5):1537-1542, 2016.