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On the existence of reflecting n-queens configurations,
with T. Dai.
Submitted, 9 pages. arxiv:2407.12742.
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Thresholds for (n,q,2)-Steiner systems via Refined Absorption,
with M. Delcourt and L. Postle.
Submitted, 17 pages. arxiv:2402.17858.
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Clique decompositions in random graphs via Refined Absorption,
with M. Delcourt and L. Postle.
Submitted, 49 pages. arxiv:2402.17857.
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Subsquares in random Latin squares and rectangles,
with A. Divoux, C. Kennedy, J. Sidhu.
Submitted, 13 pages. arxiv:2311.04152.
- Based on work done during the Georgia Tech School of Mathematics Summer 2023 REU.
- Slides from Alex's talk in the GT Graph Theory seminar.
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The independence ratio of 4-cycle-free planar graphs,
with S. Kolichala, C. McFarland, and J. Su.
Submitted, 12 pages. arxiv:2305.02414.
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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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Fractional vertex-arboricity of planar graphs,
with M. Bonamy, F. Kardos, and L. Postle.
Submitted, 14 pages. arXiv:2009.12189.
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The local fractional Brooks' Theorem,
with L. Postle.
Based on
arxiv:1811.11806v1.
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Optimal spread for spanning subgraphs of Dirac hypergraphs,
with A. Müyesser and A. Pokrovskiy.
Journal of Combinatorial Theory, Series B,
169:507-541, 2024
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Perfect matchings in random sparsifications of Dirac hypergraphs,
with D. Kang, D. Kühn, D. Osthus, and V. Pfenninger.
Combinatorica,
advance online publication.
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Fractional coloring with local demands and applications to degree-sequence bounds on the independence number,
with L. Postle.
Journal of Combinatorial Theory, Series B,
169:298-337, 2024.
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Improving the Caro–Wei bound and applications to Turán stability,
with L. Postle.
Discrete Applied Mathematics,
358:33-43, 2024.
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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.
Combinatorics, Probability, and Computing,
33(2):179-195, 2024.
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A proof of the Erdős-Faber-Lovász conjecture,
with D. Kang, D. Kühn, A. Methuku, and D. Osthus.
Annals of Mathematics,
198(2):537-618, 2023.
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Graph and hypergraph colouring via nibble methods: A survey,
with D. Kang, D. Kühn, A. Methuku, and D. Osthus.
Proceedings of the 8th European Congress of Mathematics,
771-823, 2023.
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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.
Transactions of the American Mathematical Society,
376(9):6623-6662, 2023.
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On the density of critical graphs with no large cliques,
with L. Postle.
Combinatorica,
43:57–89, 2023.
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Hamilton transversals in random Latin squares,
with S. Gould.
Random Structures & Algorithms,
67(2):450-478, 2023.
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Bounding χ by a fraction of Δ for graphs without large cliques,
with M. Bonamy, P. Nelson, and L. Postle.
Journal of Combinatorial Theory, Series B,
157:263-282, 2022.
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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.