Richard Mycroft

Accepting PhD Students

PhD projects

Richard Mycroft’s primary research interests lie in the field of extremal graph theory, in which he has worked on a variety of embedding problems. His most recent research develops the theory of matching and packings in uniform hypergraphs, in the presence of various minimum degree conditions. He has also previously considered Hamiltonicity of uniform hypergraphs in a similar manner. Another focus of his research is the problem of embedding trees in directed graphs; the highlight of his work on this topic so far was proving Sumner’s universal tournament conjecture for any sufficiently large tournament. However, this milestone is by no means the end of his interest in this topic; it continues to be an active area of research.

Research activity per year

18 Article
2 Chapter
1 Conference contribution
1 Review article
More
- 1 Working paper

23 results

2024
Matchings in multipartite hypergraphs
Bowtell, C. & Mycroft, R., 24 Sept 2024, (Accepted/In press) In: Combinatorial Theory.
Research output: Contribution to journal › Review article › peer-review

Open Access
2019
Classification of Maximum Hittings by Large Families
Bowtell, C. & Mycroft, R., 16 Nov 2019, In: Graphs and Combinatorics. 36, p. 27-39 13 p.
Research output: Contribution to journal › Article › peer-review
2018
Contagious sets in a degree-proportional bootstrap percolation process
Garbe, F., McDowell, A. & Mycroft, R., 29 Oct 2018, In: Random Structures and Algorithms. 53, 4, p. 638-651
Research output: Contribution to journal › Article › peer-review

Open Access
File
186 Downloads (Pure)
Hamilton cycles in hypergraphs below the Dirac threshold
Garbe, F. & Mycroft, R., 9 May 2018, (E-pub ahead of print) In: Journal of Combinatorial Theory. Series B.
Research output: Contribution to journal › Article › peer-review

Open Access
File
3 Citations (Scopus)

318 Downloads (Pure)
Hamilton ℓ-Cycles in Randomly Perturbed Hypergraphs
McDowell, A. & Mycroft, R., 16 Nov 2018, In: Electronic Journal of Combinatorics. 25, 4, 30 p., P4.36.
Research output: Contribution to journal › Article › peer-review

Open Access
File
9 Citations (Scopus)

74 Downloads (Pure)
Triangle-tilings in graphs without large independent sets
Balogh, J., McDowell, A., Molla, T. & Mycroft, R., 9 May 2018, (E-pub ahead of print) In: Combinatorics, Probability and Computing. 24 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
6 Citations (Scopus)

237 Downloads (Pure)
Unavoidable trees in tournaments
Mycroft, R. & Naia Dos Santos, T., 9 Feb 2018, (E-pub ahead of print) In: Random Structures and Algorithms. 29 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
3 Citations (Scopus)

211 Downloads (Pure)
2017
An asymptotic multipartite Kühn-Osthus theorem
Martin, R., Mycroft, R. & Skokan, J., 13 Jul 2017, In: SIAM Journal on Discrete Mathematics. 31, 3, p. 1498-1513 16 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
1 Citation (Scopus)

242 Downloads (Pure)
The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph
Cooley, O. & Mycroft, R., Jun 2017, In: Discrete Mathematics. 340, 6, p. 1172-1179 8 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
3 Citations (Scopus)

198 Downloads (Pure)
Tight cycles and regular slices in dense hypergraphs
Allen, P., Böttcher, J., Cooley, O. & Mycroft, R., Jul 2017, In: Journal of Combinatorial Theory, Series A. 149, p. 30-100 71 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
7 Citations (Scopus)

172 Downloads (Pure)
2016
Hamilton cycles in quasirandom hypergraphs
Lenz, J., Mubayi, D. & Mycroft, R., 26 Feb 2016, (E-pub ahead of print) In: Random Structures and Algorithms.
Research output: Contribution to journal › Article › peer-review

Open Access
File
3 Citations (Scopus)

210 Downloads (Pure)
Packing k-partite k-uniform hypergraphs
Mycroft, R., Feb 2016, In: Journal of Combinatorial Theory, Series A. 138, p. 60-132 73 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
15 Citations (Scopus)

271 Downloads (Pure)
The Complexity of the Hamilton Cycle Problem in Hypergraphs of High Minimum Codegree
Garbe, F. & Mycroft, R., 16 Feb 2016, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Ollinger, N. & Vollmer, H. (eds.). Dagstuhl, Germany: Schloss Dagstuhl, Vol. 47. p. 1-13 13 p. 38. (Leibniz International Proceedings in Informatics (LIPIcs); vol. 47).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Open Access
File
2 Citations (Scopus)

77 Downloads (Pure)
2015
A geometric theory for hypergraph matching
Keevash, P. & Mycroft, R., 2015, A geometric theory for hypergraph matching. American Mathematical Society, Vol. 233. 101 p. Chapter 6
Research output: Chapter in Book/Report/Conference proceeding › Chapter
16 Citations (Scopus)

20 Downloads (Pure)
A Multipartite Hajnal-Szemerédi Theorem
Keevash, P. & Mycroft, R., Sept 2015, In: Journal of Combinatorial Theory. Series B. 114, p. 187-236 50 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
11 Citations (Scopus)

178 Downloads (Pure)
Polynomial-time perfect matchings in dense hypergraphs
Keevash, P., Knox, F. & Mycroft, R., 10 Jan 2015, In: Advances in Mathematics. 269, p. 265-334 70 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
11 Citations (Scopus)

247 Downloads (Pure)
2014
A random version of Sperner's theorem
Balogh, J., Mycroft, R. & Treglown, A., Nov 2014, In: Journal of Combinatorial Theory, Series A. 128, p. 104-110 7 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
8 Citations (Scopus)

200 Downloads (Pure)
2013
A Geometric Theory for Hypergraph Matching
Keevash, P. & Mycroft, R., 9 Oct 2013, Cornell University Library, 101 p.
Research output: Working paper/Preprint › Working paper
Polynomial-time perfect matchings in dense hypergraphs
Keevash, P., Knox, F. & Mycroft, R., 2013, Proceedings of the Annual ACM Symposium on Theory of Computing. p. 311-320 10 p.
Research output: Chapter in Book/Report/Conference proceeding › Chapter
3 Citations (Scopus)
2011

An approximate version of Sumner's universal tournament conjecture☆
Kuhn, D., Mycroft, R. & Osthus, D., 26 Jan 2011, In: Journal of Combinatorial Theory. Series B. 101, p. 415-447 33 p.
Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)
A proof of Sumner's universal tournament conjecture for large tournaments
Kuhn, D., Mycroft, R. & Osthus, D., 1 Apr 2011, In: London Mathematical Society. Proceedings . 102, p. 731-766 36 p.
Research output: Contribution to journal › Article › peer-review
16 Citations (Scopus)
Loose Hamilton cycles in hypergraphs
Keevash, P., Kuhn, D., Mycroft, R. & Osthus, D., 1 Apr 2011, In: Discrete Mathematics. 311, 7, p. 544-559 16 p.
Research output: Contribution to journal › Article › peer-review
39 Citations (Scopus)
2010
Hamilton l-cycles in uniform hypergraphs
Kuhn, D., Mycroft, R. & Osthus, D., 1 Oct 2010, In: Journal of Combinatorial Theory, Series A. 117, 7, p. 910-927 18 p.
Research output: Contribution to journal › Article › peer-review
41 Citations (Scopus)

Richard Mycroft

Research output

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