Preprints & Articles

Preprints

• S. Berger, J. Lee, M. Schacht, Odd cycles in subgraphs of sparse pseudorandom graphs, submitted
• S. Berger, S. Piga, Chr. Reiher, V. Rödl, M. Schacht, Turán density of cliques of order five in 3-uniform hypergraphs with quasirandom links, submitted;
  Extended abstract appeared in Procedia Computer Science 195, 412-418
• E. Friedgut, E. Kuperwasser, W. Samotij, M. Schacht, Sharp thresholds for Ramsey properties, submitted
• B. Nagle, V. Rödl, M. Schacht, Equivalent regular partitions of 3-uniform hypergraphs, submitted

• M. Schacht, Restricted problems in extremal combinatorics, Proceedings of the ICM 2022, to appear

Published

• P. Araújo, S. Piga, M. Schacht, Localized codegree conditions for tight Hamilton cycles in 3-uniform hypergraphs, SIAM Journal on Discrete Mathematics 36(1), 2022, 147-169;
  Extended abstract appeared in Acta Math. Univ. Comenian. (N.S.) 88(3), 389-394
• Chr. Reiher, V. Rödl, M. Sales, K. Sames, M. Schacht, On quantitative aspects of a canonisation theorem for edge-orderings, Journal of the London Mathematical Society 106(3), 2022, 2773-2803
• S. Antoniuk, A. Dudek, Chr. Reiher, A. Ruciński, M. Schacht, High powers of Hamiltonian cycles in randomly augmented graphs, Journal of Graph Theory 98(2), 2021, 255-284
• D. Bal, R. Berkowitz, P. Devlin, M. Schacht, Hamiltonian Berge cycles in random hypergraphs, Combinatorics, Probability and Computing 30(2), 2021, 228-238
• D. Clemens, M. Miralaei, D. Reding, M. Schacht, A. Taraz, On the size-Ramsey number of grid graphs, Combinatorics, Probability and Computing 30(5), 2021, 670-685
• H. Hàn, T. Retter, V. Rödl, M. Schacht, Ramsey-type numbers involving graphs and hypergraphs with large girth, Combinatorics, Probability and Computing 30(5), 2021, 722-740;
  Extended abstract appeared in Electron. Notes Discrete Math. 50, 457-463
• A. Dudek, Chr. Reiher, A. Ruciński, M. Schacht, Powers of Hamiltonian cycles in randomly augmented graphs, Random Structures and Algorithms 56(1), 2020, 122-141
• O. Ebsen, G. S. Maesaka, Chr. Reiher, M. Schacht, B. Schülke, Embedding spanning subgraphs in uniformly dense and inseparable graphs, Random Structures and Algorithms 57(4), 2020, 1077-1096;
  Extended abstract appeared in Acta Math. Univ. Comenian. (N.S.) 88(3), 637-641
• O. Ebsen, M. Schacht, Homomorphism thresholds for odd cycles, Combinatorica 40(1), 2020, 39-62
• B. Narayanan, M. Schacht, Sharp thresholds for nonlinear Hamiltonian cycles in hypergraphs, Random Structures and Algorithms 57(1), 2020, 244-255
• H. Oberkampf, M. Schacht, On the structure of dense graphs with bounded clique number, Combinatorics, Probability and Computing 29(5), 2020, 641-649
• J. Polcyn, Chr. Reiher, V. Rödl, A. Ruciński, M. Schacht, B. Schülke, Minimum pair degree condition for tight Hamiltonian cycles in 4-uniform hypergraphs, Acta Mathematica Hungarica 161(2), 2020, 647-699
  Extended abstract appeared in Acta Math. Univ. Comenian. (N.S.) 88(3), 1023-1027
• W. Bedenknecht, G. O. Mota, Chr. Reiher, M. Schacht, On the local density problem for graphs of given odd-girth, Journal of Graph Theory 90(2), 2019, 137-149;
  Extended abstract appeared in Electron. Notes Discrete Math. 62, 39-44
• Y. Kohayakawa, G. O. Mota, M. Schacht, Monochromatic trees in random graphs, Mathematical Proceedings of the Cambridge Philosophical Society 166(1), 2019, 191-208;
  Extended abstract appeared in Electron. Notes Discrete Math. 61, 759-764
• Chr. Reiher, M. Schacht, Forcing quasirandomness with triangles, Forum of Mathematics, Sigma 7(e9), 2019, 19 pages
• Chr. Reiher, V. Rödl, A. Ruciński, M. Schacht, E. Szemerédi, Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs, Proceedings of the London Mathematical Society (3), 119(2), 2019, 409-439
• E. Aigner-Horev, D. Conlon, H. Hàn, Y. Person, M. Schacht, Quasirandomness in hypergraphs, Electronic Journal of Combinatorics 25(3.34), 2018, 22pp.
  Extended abstract appeared in Electron. Notes Discrete Math. 61, 13-19
• J. de O. Bastos, G. O. Mota, M. Schacht, J. Schnitzer, F. Schulenburg, Loose Hamiltonian cycles forced by large (k-2)-degree – sharp version, Contributions to Discrete Mathematics 13(2), 2018, 88-100;
  Extended abstract appeared in Electron. Notes Discrete Math. 61, 101-106
• B. Nagle, V. Rödl, M. Schacht, An algorithmic hypergraph regularity lemma, Random Structures and Algorithms 52(2), 2018, 301-353;
  Extended abstract appeared in Proceedings of SODA 2016, 1765-1773
• Chr. Reiher, V. Rödl, M. Schacht, On a Turán problem in weakly quasirandom 3-uniform hypergraphs, Journal of the European Mathematical Society 20(5), 2018, 1139-1159
• Chr. Reiher, V. Rödl, M. Schacht, On a generalisation of Mantel's theorem to uniformly dense hypergraphs, International Mathematics Research Notices 2018(16), 4899-4941
• Chr. Reiher, V. Rödl, M. Schacht, Hypergraphs with vanishing Turán density in uniformly dense hypergraphs, Journal of the London Mathematical Society 97(1), 2018, 77-97
• Chr. Reiher, V. Rödl, M. Schacht, Some remarks on     , Connections in Discrete Mathematics: A Celebration of the Work of Ron Graham, Cambridge University Press, 2018, 214-239
• M. Schacht, F. Schulenburg, Sharp thresholds for Ramsey properties of strictly balanced nearly bipartite graphs, Random Structures and Algorithms 52(1), 2018, 3-40
• J. de O. Bastos, G. O. Mota, M. Schacht, J. Schnitzer, F. Schulenburg, Loose Hamiltonian cycles forced by large (k-2)-degree – approximate version, SIAM Journal on Discrete Mathematics 31(4), 2017, 2328-2347;
  Extended abstract appeared in Electron. Notes Discrete Math. 54, 325-330
• D. Conlon, D. Dellamonica Jr., Steven La Fleur, V. Rödl, M. Schacht, A note on induced Ramsey numbers, A Journey Through Discrete Mathematics (A Tribute to Jiří Matoušek), Springer, 2017, 357-366
• Y. Kohayakawa, G. O. Mota, M. Schacht, A. Taraz, Counting results for sparse pseudorandom hypergraphs I, European Journal of Combinatorics 65, 2017, 276-287
• Y. Kohayakawa, G. O. Mota, M. Schacht, A. Taraz, Counting results for sparse pseudorandom hypergraphs II, European Journal of Combinatorics 65, 2017, 288-301
  Extended abstract appeared in Electron. Notes Discrete Math. 50, 421-426
• V. Rödl, A. Ruciński, M. Schacht, An exponential-type upper bound for Folkman numbers, Combinatorica 37(4), 2017, 767-784
• V. Rödl, A. Ruciński, M. Schacht, Ramsey properties of random graphs and Folkman numbers, Discussiones Mathematicae Graph Theory 37(3), 2017, 755-776
• V. Rödl, A. Ruciński, M. Schacht, E. Szemerédi, On the Hamiltonicity of triple systems with high minimum degree, Annals of Combinatorics 21(1), 2017, 95-117
• E. Friedgut, H. Hàn, Y. Person, M. Schacht, A sharp threshold for van der Waerden's theorem in random subsets, Discrete Analysis 2016:7, 19 pp.
• Y. Kohayakawa, V. Rödl, M. Schacht, Discrepancy and Eigenvalues of Cayley Graphs, Czechoslovak Mathematical Journal 66(3), 2016, 941-954;
  Extended abstract appeared in ITI Series of Charles University 145, 242-246
• S. Messuti, V. Rödl, M. Schacht, Packing minor-closed families of graphs into complete graphs, Journal of Combinatorial Theory (B) 119, 2016, 245-265;
  Extended abstract appeared in Electron. Notes Discrete Math. 49, 651-659
• Chr. Reiher, V. Rödl, M. Schacht, Embedding tetrahedra into quasirandom hypergraphs, Journal of Combinatorial Theory (B) 121, 2016, 229-247
• Chr. Reiher, M. Schacht, Clique factors in locally dense graphs, appendix to Triangle factors of graphs without large independent sets and of weighted graphs, by J. Balogh, Th. Molla, M. Sharifzadeh, Random Structures and Algorithms 49(4), 2016, 691-693
• M. Schacht, Extremal results for random discrete structures, Annals of Mathematics 184(2), 2016, 333-365
• S. Messuti, M. Schacht, On the structure of graphs with given odd girth and large minimum degree, Journal of Graph Theory 80(1), 2015, 69-81;
  Extended abstract appeared in CRM Series, Ed. Norm. (Pisa) 16, 521-526
• G. O. Mota, G. N. Sárközy, M. Schacht, A. Taraz, Ramsey numbers for bipartite graphs with small bandwidth, European Journal of Combinatorics 48, 2015, 165-176;
  Extended abstract appeared in CRM Series, Ed. Norm. (Pisa) 16, 165-170
• E. Aigner-Horev, H. Hàn, M. Schacht, Extremal results for odd cycles in sparse pseudorandom graphs, Combinatorica 34(4), 2014, 379-406;
  Extended abstract appeared in Electron. Notes Discrete Math. 44, 385-391
• D. Conlon, W. T. Gowers, W. Samotij, M. Schacht, On the KŁR conjecture in random graphs, Israel Journal of Mathematics 203(1), 2014, 535-580
• Y. Kohayakawa, M. Schacht, R. Spöhel, Upper bounds on probability thresholds for asymmetric Ramsey properties, Random Structures and Algorithms 44(1), 2014, 1-28
• E. Buß, H. Hàn, M. Schacht, Minimum vertex degree conditions for loose Hamilton cycles in 3-uniform hypergraphs, Journal of Combinatorial Theory (B) 103(6), 2013, 658-678;
  Extended abstract appeared in Electron. Notes Discrete Math. 38, 207-212
• V. Rödl, M. Schacht, Extremal results in random graphs, Erdős Centennial, vol. 25 series, Bolyai Soc. Math. Stud., 2013, 535-583
• D. Conlon, H. Hàn, Y. Person, M. Schacht, Weak quasi-randomness for uniform hypergraphs, Random Structures and Algorithms 40(1), 2012, 1-38
• D. Dellamonica Jr., P. Haxell, T. Łuczak, D. Mubayi, B. Nagle, Y. Person, V. Rödl, M. Schacht, Tree-minimal graphs are almost regular, Journal of Combinatorics 3(1), 2012, 49-62
• D. Dellamonica Jr., P. Haxell, T. Łuczak, D. Mubayi, B. Nagle, Y. Person, V. Rödl, M. Schacht, J. Verstraëte, On even-degree subgraphs of linear hypergraphs, Combinatorics, Probability and Computing 21(1-2), 2012, 113-127
• V. Rödl, M. Schacht, Complete partite subgraphs in dense hypergraphs, Random Structures and Algorithms 41(4), 2012, 557-573
• M. Kang, O. Pikhurko, A. Ravsky, M. Schacht, O. Verbitsky, Untangling planar graphs from a specified vertex position – Hard cases, Discrete Applied Mathematics 159(8), 2011, 789-799
• Y. Kohayakawa, V. Rödl, M. Schacht, E. Szemerédi, Sparse partition universal graphs for graphs of bounded degree, Advances in Mathematics 226(6), 2011, 5041-5065
• Y. Person, M. Schacht, An expected polynomial time algorithm for coloring 2-colorable 3-graphs, Discrete Mathematics & Theoretical Computer Science 13(2), 2011, 1-18;
  Extended abstract appeared in Electron. Notes Discrete Math. 34, 465-469
• N. Alon, A. Coja-Oghlan, H. Hàn, M. Kang, V. Rödl, M. Schacht, Quasi-Randomness and Algorithmic Regularity for Graphs with General Degree Distributions, SIAM Journal on Computing 39(6), 2010, 2336-2362;
  Extended abstract appeared in Proceedings of ICALP 2007, 789-800
• E. Friedgut, V. Rödl, M. Schacht, Ramsey properties of random discrete structures, Random Structures and Algorithms 37(4), 2010, 407-436
• H. Hàn, M. Schacht, Dirac-type results for loose Hamilton cycles in uniform hypergraphs, Journal of Combinatorial Theory (B) 100(3), 2010, 332-346
• J. Hladký, M. Schacht, Note on bipartite graph tilings, SIAM Journal on Discrete Mathematics 24(2), 2010, 357-362
• Y. Kohayakawa, B. Nagle, V. Rödl, M. Schacht, Weak regularity and linear hypergraphs, Journal of Combinatorial Theory (B) 100(2), 2010, 151-160
• Y. Kohayakawa, V. Rödl, M. Schacht, J. Skokan, On the triangle removal lemma for subgraphs of sparse pseudorandom graphs, An Irregular Mind (Szemerédi is 70), vol. 21 series (2010) Bolyai Soc. Math. Stud., 359-404
• H. Lefmann, Y. Person, M. Schacht, A structural result for hypergraphs with many restricted edge colorings, Journal of Combinatorics 1(3-4), 2010, 441-475
• V. Rödl, M. Schacht, Regularity lemmas for graphs, Fete of Combinatorics and Computer Science, vol. 20 series (2010) Bolyai Soc. Math. Stud., 287-325
• J. Böttcher, M. Schacht, A. Taraz, Proof of the bandwidth conjecture of Bollobás and Komlós, Mathematische Annalen 343(1), 2009, 175-205;
  Extended abstract appeared in Electron. Notes Discrete Math. 29, 485-489
• H. Hàn Y. Person, M. Schacht, On perfect matchings in uniform hypergraphs with large minimum vertex degree, SIAM Journal on Discrete Mathematics 23(2), 2009, 732-748
• H. Lefmann, Y. Person, V. Rödl, M. Schacht, On colorings of hypergraphs without monochromatic Fano planes, Combinatorics, Probability and Computing 18(5), 2009, 803-818
• V. Rödl, M. Schacht, Generalizations of the removal lemma, Combinatorica 29(4), 2009, 467-501;
  Extended abstract appeared in Proceedings of STOC 2007, 488-495
• J. Böttcher, M. Schacht, A. Taraz, Spanning 3-colourable subgraphs of small bandwidth in dense graphs, Journal of Combinatorial Theory (B) 98(4), 2008, 752-777;
  Extended abstract appeared in Proceedings of SODA 2007, 618-626
• B. Nagle, S. Olsen, V. Rödl, M. Schacht, On the Ramsey number of sparse 3-graphs, Graphs and Combinatorics 24(3), 2008, 205-228
• B. Nagle, V. Rödl, M. Schacht, Note on the 3-graph counting lemma, Discrete Mathematics 308(19), 2008, 4501-4517
• V. Rödl, A. Ruciński, M. Schacht, E. Szemerédi, A note on perfect matchings in uniform hypergraphs with large minimum collective degree, Commentationes Mathematicae Universitatis Carolinae 49(4), 2008, 633-636
• Chr. Avart, V. Rödl, M. Schacht, Every monotone 3-graph property is testable, SIAM Journal on Discrete Mathematics 21(1), 2007, 73-92;
  Extended abstract appeared in: Electron. Notes Discrete Math. 22, 539-542
• B. Bollobás, Y. Kohayakawa, V. Rödl, M. Schacht, A. Taraz, Essentially infinite colourings of hypergraphs, Proceedings of the London Mathematical Society 95(3), 2007, 709-734;
  Extended abstract appeared in: Electron. Notes Discrete Math. 19, 179-185
• Y. Kohayakawa, V. Rödl, M. Schacht, P. Sissokho, J. Skokan, Turán's theorem for pseudo-random graphs, Journal of Combinatorial Theory (A) 114(4), 2007, 631-657
• V. Rödl, M. Schacht, Regular partitions of hypergraphs: Regularity Lemmas, Combinatorics, Probability and Computing 16(6), 2007, 833-885
• V. Rödl, M. Schacht, Regular partitions of hypergraphs: Counting Lemmas, Combinatorics, Probability and Computing 16(6), 2007, 887-901
• V. Rödl, A. Ruciński, M. Schacht, Ramsey properties of random k-partite k-uniform hypergraphs, SIAM Journal on Discrete Mathematics 21(2), 2007, 442-460
• V. Rödl, M. Schacht, M. Siggers, N. Tokushige, Integer and fractional packings of hypergraphs, Journal of Combinatorial Theory (B) 97(2), 2007, 245-268
• J. Bang-Jensen, B. Reed, R. Šámal, M. Schacht, B. Toft, U. Wagner, On six problems posed by Jarik Nešetřil, Topics in Discrete Mathematics, vol. 26 series (2006) Algorithms Combin., 613-627
• B. Nagle, V. Rödl, M. Schacht, The counting lemma for regular k-uniform hypergraphs, Random Structures and Algorithms 28(2), 2006, 113-179
• B. Nagle, V. Rödl, M. Schacht, Extremal hypergraph problems and the regularity method, Topics in Discrete Mathematics, vol. 26 series (2006) Algorithms Combin., 247-278
• V. Rödl, M. Schacht, E. Tengan, N. Tokushige, Density theorems and extremal hypergraph problems, Israel Journal of Mathematics 152, 2006, 371-380
• V. Rödl, B. Nagle, J. Skokan, M. Schacht, Y. Kohayakawa, The hypergraph regularity method and its applications, Proceedings of the National Academy of Sciences USA 102(23), 2005, 8109-8113
• Y. Kohayakawa, V. Rödl, M. Schacht, The Turán theorem for random graphs, Combinatorics, Probability and Computing 13(1), 2004, 61-91