Department of Mathematics
Columbia House
London School of Economics
Houghton Street
London WC2A 2AE, UK
o.parczyk@lse.ac.uk
arXiv, Google Scholar, ORCiD
I am a visiting fellow in the Department of Mathematics of the London School of Economics and Political Science working with Peter Allen, Julia Böttcher, and Jozef Skokan. My research is funded by a fellowship of the German Research Foundation (DFG, Grant PA 3513/11). Previously, I was a postdoctoral researcher at TU Ilmenau. I obtained my Ph.D. at Goethe University Frankfurt am Main, where my Supervisor was Yury Person. I got my Bachelors’s and Master’s degree at FU Berlin with Tibor Szabó.
Research Interests
My research interests are probabilistic and extremal combinatorics, Ramsey theory, and graph limit theory. I am mostly working on embedding type problems for graphs and usually they involve randomness in one way or the other.
Recent Contributions
 We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. More precisely, for any \(\gamma>0\) and \(k\ge3\), we show that asymptotically almost surely, every subgraph of the binomial random \(k\)uniform hypergraph \(G^{(k)}\big(n,n^{\gamma1}\big)\) in which all \((k1)\)sets are contained in at least \((1/2+\gamma)pn\) edges has a tight Hamilton cycle. This is a cyclic ordering of the \(n\) vertices such that each consecutive \(k\) vertices forms an edge.
This is joint work with Peter Allen and Vincent Pfenninger, arXiv:2105.04513.
 We study the problem of finding pairwise vertexdisjoint triangles in the randomly perturbed graph model, which is the union of any nvertex graph \(G\) with linear minimum degree and the binomial random graph \(G(n,p)\). We prove that asymptotically almost surely \(G \cup G(n,p)\) contains \(\min\{\delta(G), \lceil n/3 \rceil \}\) pairwise vertexdisjoint triangles, provided that \(p \ge C\, \log n/n\), where \(C\) is a large enough constant. This resolves the last open case for the existence of trianglefactors in randomly perturbed graphs.
This is joint work with Julia Böttcher, Amedeo Sgueglia, and Jozef Skokan, arXiv:2011.07612.
Upcoming Events
Publications
Preprints
 Resilience for tight Hamiltonicity with Peter Allen and Vincent Pfenninger. arXiv:2105.04513.
 Triangles in randomly perturbed graphs with Julia Böttcher, Amedeo Sgueglia, and Jozef Skokan. arXiv:2011.07612.
 Near optimal sparsityconstrained group testing: improved bounds with Oliver Gebhard, Max HahnKlimroth, Manuel Penschuck, Maurice Rolvien, Jonathan Scarlett, and Nelvin Tan. arXiv:2004.11860.
 AntiRamsey threshold of complete graphs for sparse graphs with Yoshiharu Kohayakawa, Guilherme O. Mota, and Jakob Schnitzer. arXiv:1902.00306.
To appear
 Positional games on randomly perturbed graphs with Dennis Clemens, Fabian Hamann, and Yannick Mogge, to appear in SIAM Journal on Discrete Mathematics. arXiv:2009.14583.
 AntiRamsey threshold of cycles with Garbiel F. Barros, Bruno P. Cavalar, and Guilherme O. Mota, to appear in Discrete Applied Mathematics. arXiv:2006.02079.
Published

The sizeRamsey number of 3uniform tight paths with Jie Han, Yoshiharu Kohayakawa, Shoham Letzter, and Guilherme O. Mota, Advances in Combinatorics, 2021:5, 12pp. DOI, arXiv.

Random perturbation of sparse graphs with Max HahnKlimroth, Giulia S. Maesaka, Yannick Mogge, and Samuel Mohr, The Electronic Journal of Combinatorics (2021), no 2, P2.26. DOI, arXiv.

The sizeRamsey number of powers of bounded degree trees with Sören Berger, Yoshiharu Kohayakawa, Giulia S. Maesaka, Taísa Martins, Walner Mendonça, and Guilherme O. Mota. Journal of the London Mathematical Society, (2020), 1–19. DOI, arXiv.

Finding tight Hamilton cycles in random hypergraphs faster with Peter Allen, Christoph Koch, and Yury Person. Combinatorics, Probability and Computing 30 (2021), no 2, 239–257. DOI, arXiv.

Embedding spanning bounded degree graphs in randomly perturbed graphs with Julia Böttcher, Richard Montgomery, and Yury Person. Mathematika 66 (2020), no 2, 422–447. DOI, arXiv.

2universality in randomly perturbed graphs. European Journal of Combinatorics 87 (2020), 103–118. DOI, arXiv.

Semirandom graph process with Omri Ben Eliezer, Dan Hefetz, Gal Kronenberg, Clara Shikelman, and Miloš Stojaković. Random Structures & Algorithms 56 (2020), no 3, 648–675. DOI, arXiv.

Universality of bounded degree spanning trees in randomly perturbed graphs with Julia Böttcher, Jie Han, Yoshiharu Kohayakawa, Richard Montgomery, and Yury Person. Random Structures & Algorithms 55 (2019), no 4, 854–864. DOI, arXiv.

Spanning structures and universality in sparse hypergraphs with Yury Person. Random Structures & Algorithms 49 (2016), no 4, 819–844. DOI, arXiv.

On universal hypergraphs with Samuel Hetterich and Yury Person. The Electronic Journal of Combinatorics (2016), no 4, P4.28. DOI, arXiv.
Conference Proceedings
 The square of a Hamilton cycle in randomly perturbed graphs with Julia Böttcher, Amedeo Sgueglia, and Jozef Skokan, EUROCOMB 2021
 WaiterClient Games on Randomly Perturbed Graphs with Dennis Clemens, Fabian Hamann, and Yannick Mogge, EUROCOMB 2021.
 Cycle factors in randomly perturbed graphs with Julia Böttcher, Amedeo Sgueglia, and Jozef Skokan, LAGOS 2021
 The sizeRamsey number of powers of bounded degree trees with Sören Berger, Yoshiharu Kohayakawa, Giulia S. Maesaka, Taísa Martins, Walner Mendonça, and Guilherme O. Mota. Acta Mathematica Universitatis Comenianae 88 (2019), no 3, 451–456. URL.
 More nonbipartite forcing pairs with Tamas Hubai, Dan Král, and Yury Person. Acta Mathematica Universitatis Comenianae 88 (2019), no 3, 819–825. URL, arXiv.
 Almost spanning universality in random graphs. Acta Mathematica Universitatis Comenianae 88 (2019), no 3, 997–1002. URL.
 AntiRamsey threshold of cycles for sparse graphs with Gabriel F. Barros, Bruno P. Cavalar, and Guilherme O. Mota. Electronic Notes in Theoretical Computer Science 346 (2019), 89–98. DOI, arXiv.
 Finding tight Hamilton cycles in random hypergraphs faster with Peter Allen, Christoph Koch, and Yury Person. LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science, vol 10807. Springer, Cham. DOI.
 Embedding spanning bounded degree subgraphs in randomly perturbed graphs with Julia Böttcher, Richard Montgomery, and Yury Person. Electronic Notes in Discrete Mathematics 61 (2017), 155–161. DOI.
 On spanning structures in random hypergraphs with Yury Person. Electronic Notes in Discrete Mathematics 49 (2015), 611–619. DOI.
Teaching
 Graph theory (shared lecture), London Taught Course Centre, MT 2020
 Calculus II (TA), TU Ilmenau, ST 2019
 Discrete Mathematics (shared lecture), TU Ilmenau, WT 2018
 Calculus I (TA), TU Ilmenau, WT 2018
 Discrete Mathematics (TA), Goethe Universität Frankfurt, ST 2017
 Optimisation (TA), Goethe Universität Frankfurt, WT 2016
 Discrete Mathematics I (TA), FU Berlin, ST 2014
 Stochastic I (TA), FU Berlin, WT 2013
 Mathematics for ComputerScientists II (TA), FU Berlin, ST 2013
 Mathematics for ComputerScientists I,III (TA), FU Berlin, WT 2012
 Mathematics for ComputerScientists II(TA), FU Berlin, ST 2012
 Mathematics for ComputerScientists I (TA), FU Berlin, WT 2011
 Mathematics for Physicists (TA), FU Berlin, ST 2011
Past Events
 2021 Colloquia in Combinatorics (online), London (UK), 1213 May 2021.
 DMV Annual Meeting 2020 (online), Chemnitz (Germany), 1417 September 2020.
 Workshop on Graph Theory & Combinatorics in Thuringia (online), Erfurt (Germany), 2831 July 2020.
 Workshop Cycles & Colourings, High Tatras (Slovakia), 26 September 2019.
 EUROCOMB 2019, Bratislava (Slovakia), 2630 August 2019
 RS&A 2019, Zurich (Switzerland), 1519 July 2019
 ILKE6 Workshop, Košice (Slovakia), 2226 July 2019
 Visiting USP, São Paulo (Brazil), January 2019
 Workshop on structure and randomness in hypergraphs, London (UK), 1721 December 2018
 Kolloquium über Kombinatorik 2018, Paderborn (Germany), 2324 November 2018
 First Southwestern German Workshop on Graph Theory, Karlsruhe (Germany), 2731 August 2018
 Prague summer school on discrete mathematics, Prague (Czech Republic), 1620 July 2018
 Large networks and random graphs, Frankfurt (Germany), 913 July 2018
 EUROCOMB 2017, Vienna (Austria), 1 September  8 August 2017
 RS&A 2017, Gniezno (Poland), 711 August 2017
 Visiting USP, São Paulo (Brazil), March 2017
 LargeScale Structures in Random Graphs Workshop, London (UK), 1216 December 2016
 6th Polish Combinatorial Conference, Będlewo (Poland), 1923 September 2016
 AGWorkshop, Hirschegg (Austria), 2226 August 2016
 7ECM, Berlin (Germany), 1822 July 2016
 TAU  FUB Workshop on Positional Games, Berlin (Germany), 2226 February 2016
 Visiting USP, São Paulo (Brazil), January 2016
 Kolloquium über Kombinatorik 2015, Ilmenau (Germany), 67 November 2015
 Cargèse fall school on random graphs, Corsica (France), 2026 September 2015
 EUROCOMB 2015, Bergen (Norway), 4 September  31 August 2015
 RS&A 2015, Pittsburgh (USA), 2127 July 2015
 Research School Regularity and Analytic Methods in Combinatorics, Warwick (UK), 15 July 2015
 BerlinPoznanHamburg Seminar on Discrete Mathematics, Berlin (Germany), 2930 May 2015
 BerlinPoznan Seminar on Discrete Mathematics, Hamburg (Germany), 2324 May 2014
Talks
 Between probabilistic and extremal graph theory at Algorithm Engineering Group Research Seminar at HassoPlattnerInstitut in 2021
 Resilience for tight Hamilton cycles in random hypergraphs at the Graz Combinatorics and Optimization Seminar in 2020 and the Online Mittagsseminar der Gruppe Diskrete Mathematik at TUIlmenau in 2021
 Factors in randomly perturbed graphs at the Minisymposium Extremal and Probabilistic Combinatorics in the DMV Annual Meeting 2020 at TU Chemnitz
 The sizeRamsey number of tight 3uniform paths at C&C 2019, Research Seminars at LSE, FU Berlin, and TU Ilmenau in 2019, and at Warwick University in 2020
 More nonbipartite forcing pairs at EUROCOMB 2019
 Almost spanning universality in random graphs at EUROCOMB 2019
 Universality in randomly perturbed graphs at RS&A 2019
 The sizeRamsey number of powers of bounded degree trees at TU Ilmenau in 2019
 Universality in randomly perturbed graphs at KolKom 2018
 Randomly perturbed graphs in the Mittagsseminar at ETH Zürich, at PhD Seminar on Combinatorics, Games and Optimisation at LSE, at Large networks and random graphs workshop in Frankfurt, and at First Southwestern German Workshop on Graph Theory in 2018
 Embedding spanning bounded degree subgraphs in randomly perturbed graphs at Combinatorics Seminar at the University of Warwick in 2017 and at EUROCOMB 2017
 Finding tight Hamilton cycles in hypergraphs faster at RS&A 2017
 Explicit construction of universal hypergraphs at PhD Seminar on Combinatorics, Games and Optimisation at LSE in 2017
 Universality in random and sparse hypergraphs at Extremal graph theory seminar at The Czech Academy of Sciences in 2017
 Explicit construction of universal hypergraphs at 6th Polish Combinatorial Conference in 2016
 Universality in random and sparse hypergraphs at KolKom 2015, in the Research Seminar Combinatorics at FU Berlin in 2015, and at USP in 2016
 On Spanning Structures in Random Hypergraphs at EUROCOMB 2015
 Spanning structures and universality in sparse random hypergraphs at RS&A 2015 and Kolloquium Mathematische Informatik at Goethe University Frankfurt in 2015
 On Sidorenko’s conjecture at Research Seminar Discrete Mathematics Goethe University Frankfurt in 2014
 Relative Entropy and Sidorenko’s conjecture at Research Seminar Combinatorics at FU Berlin in 2014
 On the logarithmic calculus and Sidorenko’s conjecture at Research Seminar Combinatorics at FU Berlin in 2014
Theses
 Doctoral thesis: Spanning structures in random graphs and hypergraphs, Goethe Universität Frankfurt am Main, 2017.
 Master’s thesis: On Sidorenko’s conjecture, Freie Universität Berlin, 2014.
 Bachelor’s thesis: Kombinatorischer Nullstellensatz, Freie Universität Berlin, 2013.
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