Daniela Kühn Publications

• Perfect matchings in random sparsifications of Dirac hypergraphs (with Dong-Yeap Kang, Tom Kelly, Deryk Osthus and Vincent Pfenninger)
• Solution to a problem of Erdős on the chromatic index of hypergraphs with bounded codegree (with Dong-Yeap Kang, Tom Kelly, Abhishek Methuku and Deryk Osthus)
• A special case of Vu's conjecture: Coloring nearly disjoint graphs of bounded maximum degree (with Tom Kelly and Deryk Osthus)
• New bounds on the size of nearly perfect matchings in almost regular hypergraphs (with Dong-Yeap Kang, Abhishek Methuku and Deryk Osthus)
• A characterization of testable hypergraph properties (with Felix Joos, Jaehoon Kim and Deryk Osthus).
  An extended abstract of this paper appeared at FOCS 2017.

• Thresholds for Latin squares and Steiner triple systems: Bounds within a logarithmic factor (with Dong-Yeap Kang, Tom Kelly, Abhishek Methuku and Deryk Osthus, Transactions of the American Mathematical Society, to appear)
• A proof of the Erdős-Faber-Lovász conjecture (with Dong-Yeap Kang, Tom Kelly, Abhishek Methuku and Deryk Osthus, Annals of Mathematics, to appear)
  An extended abstract of this paper appeared at FOCS 2021.
• Hamiltonicity of random subgraphs of the hypercube (with Padraig Condon, Alberto Espuny Díaz, Antonió Girão and Deryk Osthus, Memoirs of the American Mathematical Society, to appear).
  An extended abstract of this paper appeared at SODA 2021.
• Graph and hypergraph colouring via nibble methods: a survey (with Dong-Yeap Kang, Tom Kelly, Abhishek Methuku and Deryk Osthus, Proceedings of the 8th European Congress of Mathematics, to appear)
• Hypergraph regularity and random sampling (with Felix Joos, Jaehoon Kim, and Deryk Osthus, Random Structures and Algorithms, to appear).

• The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F (with Stefan Glock, Allan Lo and Deryk Osthus, Memoirs of the American Mathematical Society 284 (2023), monograph 1406)
  A shorter version which proves the case when F is a clique (i.e. a proof for the existence of designs) can be found here.
• Path decompositions of tournaments (with Antonió Girão, Bertille Granet, Allan Lo and Deryk Osthus, Proceedings London Mathematical Society 126 (2023), 429-517)

• Almost all optimally coloured complete graphs contain a rainbow Hamilton path (with Stephen Gould, Tom Kelly and Deryk Osthus, J. Combinatorial Theory Series B 156 (2022), 57-100)

• Resolution of the Oberwolfach problem (with Stefan Glock, Felix Joos, Jaehoon Kim and Deryk Osthus, Journal of the European Mathematical Society 23 (2021), 2511–2547)
• Counting Hamilton cycles in Dirac hypergraphs (with Stefan Glock, Stephen Gould, Felix Joos and Deryk Osthus, Combinatorics, Probability, Computing 30 (2021), 631-653)
• Extremal aspects of graph and hypergraph decomposition problems (with Stefan Glock and Deryk Osthus, Surveys in Combinatorics, London Mathematical Society Lecture Note Series 470, Cambridge University Press (2021), 235-266)
• Dirac's theorem for random regular graphs (with Padraig Condon, Alberto Espuny Díaz, Antonió Girão and Deryk Osthus, Combinatorics, Probability and Computing 30 (2021), 17-36)
• Path and cycle decompositions of dense graphs (with Antonió Girão, Bertille Granet and Deryk Osthus, J. London Mathematical Society 104 (2021), 1085-1134)
• Decompositions into isomorphic rainbow spanning trees (with Stefan Glock, Richard Montgomery and Deryk Osthus, J. Combinatorial Theory Series B 146 (2021), 439-484)

• Euler tours in hypergraphs (with Felix Joos, Stefan Glock and Deryk Osthus, Combinatorica 40 (2020), 679–690
• Minimalist designs (with Ben Barber, Stefan Glock, Allan Lo, Richard Montgomery and Deryk Osthus, Random Structures and Algorithms 57 (2020), 47-63)
• Rainbow structures in locally bounded colourings of graphs (with Jaehoon Kim, Andrey Kupavskii and Deryk Osthus, Random Structures and Algorithms 56 (2020), 1171-1204)
• On a conjecture of Erdős on locally sparse Steiner triple systems (with Stefan Glock, Allan Lo and Deryk Osthus, Combinatorica 40 (2020), 363-403)

• Resilient degree sequences with respect to Hamilton cycles and matchings in random graphs (with Padraig Condon, Alberto Espuny Díaz, Jaehoon Kim and Deryk Osthus, Electronic Journal of Combinatorics 26 (2019), P4.54)
• Optimal packings of bounded degree trees (with Felix Joos, Jaehoon Kim, and Deryk Osthus, Journal of the European Mathematical Society 21 (2019), 3573-3647)
• Edge correlations in random regular hypergraphs and applications to subgraph testing (with Alberto Espuny Díaz, Felix Joos and Deryk Osthus, SIAM Journal Discrete Mathematics 33 (2019), 1837-1863)
• On the decomposition threshold of a given graph (with Stefan Glock, Allan Lo, Richard Montgomery and Deryk Osthus, J. Combinatorial Theory Series B 139 (2019), 47-127)
• A bandwidth theorem for approximate decompositions (with Padraig Condon, Jaehoon Kim and Deryk Osthus, Proceedings of the London Mathematical Society 118 (2019), 1393-1449)
• A blow-up lemma for approximate decompositions (with Jaehoon Kim, Deryk Osthus and Mykhaylo Tyomkyn, Transactions of the American Mathematical Society 371 (2019), 4655-4742)

• Forbidding induced even cycles in a graph: typical structure and counting (with Jaehoon Kim, Deryk Osthus and Timothy Townsend, J. Combinatorial Theory Series B 131 (2018), 170-219)

• Fractional clique decompositions of dense graphs and hypergraphs (with Ben Barber, Allan Lo, Richard Montgomery and Deryk Osthus, J. Combinatorial Theory Series B 127 (2017), 148–186)
• Clique decompositions of multipartite graphs and completion of Latin squares (with Ben Barber, Allan Lo, Deryk Osthus and Amelia Taylor, J. Combinatorial Theory Series A 151 (2017), 146–201)
• On the structure of oriented graphs and digraphs with forbidden tournaments or cycles (with Deryk Osthus, Timothy Townsend and Yi Zhao, J. Combinatorial Theory Series B 124 (2017), 88–127)

• Solution to a problem of Bollobas and Häggkvist on Hamilton cycles in regular graphs (with Allan Lo, Deryk Osthus and Katherine Staden, J. Combinatorial Theory Series B 121 (2016), 85-145)
• On the random greedy F-free hypergraph process (with Deryk Osthus and Amelia Taylor, SIAM Journal Discrete Mathematics 30 (2016), 1343-1350)
• Proof of a tournament partition conjecture and an application to 1-factors with prescribed cycle lengths (with Deryk Osthus and Timothy Townsend, Combinatorica 36 (2016), 451–469)
• Proof of the 1-factorization and Hamilton decomposition conjectures (with Bela Csaba, Allan Lo, Deryk Osthus and Andrew Treglown, Memoirs of the American Mathematical Society 244 (2016), monograph 1154, 170 pages)
• A domination algorithm for {0,1}-instances of the travelling salesman problem (with Deryk Osthus and Viresh Patel, Random Structures and Algorithms 48 (2016), 427–453)
• Bipartitions of highly connected tournaments (with Jaehoon Kim and Deryk Osthus, SIAM Journal Discrete Mathematics 30 (2016), 895-911)
• Optimal path and cycle decompositions of dense quasirandom graphs (with Stefan Glock and Deryk Osthus, J. Combinatorial Theory Series B 118 (2016), 88-108)
• Edge-decompositions of graphs with high minimum degree (with Ben Barber, Allan Lo and Deryk Osthus, Advances in Mathematics 288 (2016), 337-385)

• Arbitrary orientations of Hamilton cycles in digraphs (with Louis DeBiasio, Theodore Molla, Deryk Osthus and Amelia Taylor, SIAM Journal Discrete Mathematics 29 (2015), 1553-1584)
• Edge-disjoint Hamilton cycles in random graphs (with Fiachra Knox and Deryk Osthus, Random Structures and Algorithms 46 (2015), 397-445)
• The robust component structure of dense regular graphs and applications (with Allan Lo, Deryk Osthus and Katherine Staden, Proceedings of the London Mathematical Society 110 (2015), 19-56)

• Optimal covers with Hamilton cycles in random graphs (with Dan Hefetz, John Lapinskas and Deryk Osthus, Combinatorica 34 (2014), 573-596)
• Hamilton cycles in graphs and hypergraphs: an extremal perspective (with Deryk Osthus), Proceedings of the International Congress of Mathematicians 2014, Seoul, Korea, Vol 4, 381-406).
  A slightly expanded version of this survey can be found here.
• Proof of a conjecture of Thomassen on Hamilton cycles in highly connected tournaments (with John Lapinskas, Deryk Osthus and Viresh Patel, Proceedings of the London Mathematical Society 109 (2014), 733-762)
• Decompositions of complete uniform hypergraphs into Hamilton Berge cycles (with Deryk Osthus, J. Combinatorial Theory Series A 126 (2014), 128-135)
• Fractional and integer matchings in uniform hypergraphs (with Deryk Osthus and Timothy Townsend, European J. Combinatorics 38 (2014), 83-96)
• Hamilton decompositions of regular expanders: applications (with Deryk Osthus, J. Combinatorial Theory Series B 104 (2014), 1-27)

• Optimal packings of Hamilton cycles in graphs of high minimum degree (with John Lapinskas and Deryk Osthus, Combinatorics, Probability and Computing 22 (2013), 394-416)
• Hamilton decompositions of regular expanders: a proof of Kelly's conjecture for large tournaments (with Deryk Osthus, Advances in Mathematics 237 (2013), 62-146)
• Matchings in 3-uniform hypergraphs (with Deryk Osthus and Andrew Treglown, J. Combinatorial Theory Series B 103 (2013), 291-305)
• Embedding cycles of given length in oriented graphs (with Deryk Osthus and Diana Piguet, European J. Combinatorics 34 (2013), 495-501)

• On Posa's conjecture for random graphs (with Deryk Osthus, SIAM Journal Discrete Mathematics 26 (2012), 1440-1457)
• Edge-disjoint Hamilton cycles in graphs (with Demetres Christofides and Deryk Osthus, J. Combinatorial Theory Series B 102 (2012), 1035-1060)
• Finding Hamilton cycles in robustly expanding digraphs (with Demetres Christofides, Peter Keevash and Deryk Osthus, J. Graph Algorithms and Applications 16 (2012), 337-360)
• A survey on Hamilton cycles in directed graphs (with Deryk Osthus, European J. Combinatorics 33 (2012), 750-766)
• Approximate Hamilton decompositions of random graphs (with Fiachra Knox and Deryk Osthus, Random Structures and Algorithms 40 (2012), 133-149)

• An approximate version of Sumner's universal tournament conjecture (with Richard Mycroft and Deryk Osthus, J. Combinatorial Theory Series B 101 (2011), 415-447)
• A proof of Sumner's universal tournament conjecture for large tournaments (with Richard Mycroft and Deryk Osthus, Proceedings of the London Mathematical Society 102 (2011), 731-766)
• Loose Hamilton cycles in hypergraphs (with Peter Keevash, Richard Mycroft and Deryk Osthus, Discrete Mathematics 311 (2011), 544-559)

• Hamilton l-cycles in uniform hypergraphs (with Richard Mycroft and Deryk Osthus, J. Combinatorial Theory Series A 117 (2010), 910-927)
• A semi-exact degree condition for Hamilton cycles in digraphs (with Demetres Christofides, Peter Keevash and Deryk Osthus, SIAM Journal Discrete Mathematics 24 (2010), 709-756)
• Hamilton decompositions of regular tournaments (with Deryk Osthus and Andrew Treglown, Proceedings of the London Mathematical Society 101 (2010), 303-335)
• Hamiltonian degree sequences in digraphs (with Deryk Osthus and Andrew Treglown, J. Combinatorial Theory Series B 100 (2010), 367-380)
• Cycles of given length in oriented graphs (with Luke Kelly and Deryk Osthus, J. Combinatorial Theory Series B 100 (2010), 251-264)

• Minors in random regular graphs (with Nikolaos Fountoulakis and Deryk Osthus, Random Structures and Algorithms 35 (2009), 444-463)
• An Ore-type theorem for perfect packings in graphs (with Deryk Osthus and Andrew Treglown, SIAM Journal Discrete Mathematics 23 (2009), 1335-1355)
• Embedding large subgraphs into dense graphs (with Deryk Osthus, Surveys in Combinatorics (editors S. Huczynka, J. Mitchell, C. Roney-Dougal), London Math. Soc. Lecture Notes 365, Cambridge University Press, 2009, 137-167)
• Embeddings and Ramsey numbers of sparse k-uniform hypergraphs (with Oliver Cooley, Nikolaos Fountoulakis and Deryk Osthus, Combinatorica 29 (2009), 263-297)
• The minimum degree threshold for perfect graph packings (with Deryk Osthus, Combinatorica 29 (2009), 65-107)
• An exact minimum degree condition for Hamilton cycles in oriented graphs (with Peter Keevash and Deryk Osthus, Journal of the London Mathematical Society 79 (2009), 144-166)

• k-ordered Hamilton cycles in digraphs (with Deryk Osthus and Andrew Young, J. Combinatorial Theory Series B 98 (2008) 1165-1180)
• A Dirac type result for oriented graphs (with Luke Kelly and Deryk Osthus, Combinatorics, Probability and Computing 17 (2008), 689-709)
• The order of the largest complete minor in a random graph (with Nikolaos Fountoulakis and Deryk Osthus, Random Structures and Algorithms 33 (2008), 127-141)
• Linkedness and ordered cycles in digraphs (with Deryk Osthus, Combinatorics, Probability and Computing 17 (2008), 411-422)
• 3-uniform hypergraphs of bounded degree have linear Ramsey numbers (with Oliver Cooley, Nikolaos Fountoulakis and Deryk Osthus, J. Combinatorial Theory Series B 98 (2008), 484-505)
• A note on complete subdivisions in digraphs of large outdegree (with Deryk Osthus and Andrew Young, J. Graph Theory 57 (2008), 1-6)

• Perfect packings with complete graphs minus an edge (with Oliver Cooley and Deryk Osthus, European J. Combinatorics 28 (2007), 2143-2155)
• Maximizing several cuts simultaneously (with Deryk Osthus, Combinatorics, Probability and Computing 16 (2007), 277-283)

• Loose Hamilton cycles in 3-uniform hypergraphs of large minimum degree (with Deryk Osthus, J. Combinatorial Theory Series B 96 (2006), 767-821)
• Multicoloured Hamilton cycles and perfect matchings in pseudo-random graphs (with Deryk Osthus, SIAM J. Discrete Mathematics 20 (2006), 273-286)
• Improved bounds for topological cliques in graphs of large girth (with Deryk Osthus, SIAM J. Discrete Mathematics 20 (2006), 62-78)
• Matchings in hypergraphs of large minimum degree (with Deryk Osthus, J. Graph Theory 51 (2006), 269-280)
• Extremal connectivity for topological cliques in bipartite graphs (with Deryk Osthus, J. Combinatorial Theory Series B 96 (2006), 73-99)
• Critical chromatic number and the complexity of perfect packings in graphs (with Deryk Osthus, Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms 2006 (SODA), 851-859)

• Large planar subgraphs in dense graphs (with Deryk Osthus and Anusch Taraz, J. Combinatorial Theory Series B 95 (2005), 263-282)
• Spanning triangulations in graphs (with Deryk Osthus, J. Graph Theory 49 (2005), 205-233)
• Graph minor hierarchies (with Reinhard Diestel, Discrete Applied Mathematics 145 (2005), 167-182)
• Packings in dense regular graphs (with Deryk Osthus, Combinatorics, Probability and Computing 14 (2005), 325-337)
• Four-cycles in graphs without a given even cycle (with Deryk Osthus, J. Graph Theory 48 (2005), 147-156)
• Forcing unbalanced complete bipartite minors (with Deryk Osthus, European J. Combinatorics 26 (2005), 75-81)

• Complete minors in K_s,s-free graphs (with Deryk Osthus, Combinatorica 25 (2004), 49-64)
• Topological paths, cycles and spanning trees in infinite graphs (with Reinhard Diestel, European J. Combinatorics 25 (2004), 835-862)
• Induced subdivisions in K_s,s -free graphs of large average degree (with Deryk Osthus, Combinatorica 24 (2004), 287-304)
• Every graph of sufficiently large average degree contains a C₄-free graph of large average degree (with Deryk Osthus, Combinatorica 24 (2004), 155-162)
• On infinite cycles II (with Reinhard Diestel, Combinatorica 24 (2004), 91-116)
• On infinite cycles I (with Reinhard Diestel, Combinatorica 24 (2004), 69-89)
• Subdivisions of K_r+2 in graphs of average degree at least r+epsilon and large but constant girth (with Deryk Osthus, Combinatorics, Probability and Computing 13 (2004), 361-371)
• Large topological cliques in graphs without a 4-cycle (with Deryk Osthus, Combinatorics, Probability and Computing 13 (2004), 93-102)

• Partitions of graphs with high minimum degree or connectivity (with Deryk Osthus, J. Combinatorial Theory Series B 88 (2003), 29-43)
• Minors in graphs of large girth (with Deryk Osthus, Random Structures and Algorithms 22 (2003), 213-225)
• Graph-theoretical versus topological ends of graphs (with Reinhard Diestel, J. Combinatorial Theory Series B 87 (2003), 197-206)

• Topological minors in graphs of large girth (with Deryk Osthus, J. Combinatorial Theory Series B 86 (2002), 364-380)
• Forcing a K_r minor by high external connectivity (J. Graph Theory, 39 (2002), 241-264)
• On well-quasi-ordering infinite trees - Nash-Williams's theorem revisited (Math. Proc. Camb. Phil. Soc. 130 (2001), 401-408)
• Minor-universal planar graphs without accumulation points (J. Graph Theory 36 (2001), 1-7)
• A universal planar graph under the minor relation (with Reinhard Diestel, J. Graph Theory 32 (1999), 191-206)