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Research Fields and Publications


Research Fields: Combinatorics, Discrete Probability, Algorithms

  • Probabilistic Combinatorics, Analytic Combinatorics, Enumerative Combinatorics
  • Random Graphs, Random Graphs on Surfaces, Random Hypergraphs, Random Simplicial Complexes, Random Combinatorial Structures
  • Randomised Algorithms, Analysis of Algorithms

List of publications in PDF


Highlighted publications

  • Joshua Erde, Mihyun Kang, and Michael Krivelevich, Expansion in supercritical random subgraphs of the hypercube and its consequences, Annals of Probability 51 (2023), 127-156. doi:10.1214/22-AOP1592.

    • In this paper we solved an open problem posed in 1994 by Bollobás, Kohayakawa, and Łuczak, determining the diameter of the giant component of the percolated hypercube in the supercritical regime. We also gave a partial answer to a question raised in 2008 by Pete, obtaining a polynomial mixing time of the lazy random walk on the giant component.


  • Nikolaos Fountoulakis, Mihyun Kang, and Tamas Makai, Resolution of a conjecture on majority dynamics: rapid stabilisation in dense random graphs, Random Structures and Algorithms 57 (2020), 1134-1156. doi:10.1002/rsa.20970.

    • In this paper we resolved a conjecture on majority dynamics on the Erdős-Rényi random graph, which was posed in 2016 by Benjamini et al.

    We were informed by the journal Random Structures & Algorithms that this paper is among the most downloaded papers among work published between 1 January 2019 and 31 December 2020.


  • Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel, Vanishing of cohomology groups of random simplicial complexes, Random Structures and Algorithms 56 (2020), 461-500. doi:10.1002/rsa.20857.

    • In this paper we determined the sharp threshold for the vanishing of cohomology groups of random simplicial complexes which are generated by binomial random hypergraphs by taking the downward-closure. We also proved a hitting time result, relating the vanishing of the cohomology groups to the disappearance of the last minimal obstruction. In addition we determined the asymptotic distribution of the dimension of the cohomology group inside the critical window.


  • Amin Coja-Oghlan, Oliver Cooley, Mihyun Kang, and Kathrin Skubch, Core forging and local limit theorems for the k-core of random graphs, Journal of Combinatorial Theory, Series B 137 (2019), 178-231. doi:10.1016/j.jctb.2018.12.005.

    • In this paper we established local limit theorems of the k-core of the Erdős-Rényi random graph. The emergence of the k-core in a random graph is related to the `freezing phenomenon' in random boolean constraint satisfaction problems. An important ingredient to our proof is the analysis of the Warning Propagation message passing algorithm, a ubiquitous combinatorial message passing algorithm of pivotal importance to the physics view on random combinatorial structures.

    In an earlier work [Michael Behrisch, Amin Coja-Oghlan, and Mihyun Kang, Local limit theorems for the giant component of random hypergraphs, Combinatorics, Probability and Computing 23 (2014), 331-366. doi:10.1017/S0963548314000017] we derived local limit theorems for the joint distribution of the number of vertices and the number of edges in the largest component of a binomial random hypergraph.


  • Mihyun Kang and Tomasz Łuczak, Two critical periods in the evolution of random planar graphs, Transactions of the American Mathematical Society 364 (2012), 4239-4265. doi:10.1090/S0002-9947-2012-05502-4.

    • In this paper we discovered that phase transitions in random planar graphs differ significantly from the classical Erdős-Rényi random graphs. The giant component emerges when the average degree is one, but its order is about half the order of the giant component in the Erdős-Rényi random graph. In addition, the giant component covers almost all vertices, yet the 2-core is still sublinear, when the average degree is close to two but smaller than two.

    In a follow up paper [Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel, Phase transitions in graphs on orientable surfaces, Random Structures and Algorithms 56 (2020), 1117-1170. doi:10.1002/rsa.20900], we extended this work to random graphs on surfaces with constant genus.


  • Manuel Bodirsky, Éric Fusy, Mihyun Kang, and Stefan Vigerske, Boltzmann samplers, Pólya theory and cycle pointing, SIAM Journal on Computing 40 (2011), 721-769. doi:10.1137/100790082.

    • In this paper we introduced Pólya-Boltzmann samplers as a general scheme for uniform sampling of unlabelled planar graphs, planar-like graphs, and planar maps. We also introduced the cycle-pointing technique which take symmetries of graphs into consideration.


  • Mihyun Kang and Martin Loebl, The enumeration of planar graphs via Wick's theorem, Advances in Mathematics 221 (2009), 1703-1724. doi:10.1016/j.aim.2009.03.001.

    • In this paper we showed that the enumeration of graphs that are embeddable on a 2-dimensional surface can be formulated as the Gaussian matrix integral of an ice-type partition function. Some of the most puzzling conjectures of discrete mathematics are related to the notion of the cycle double cover. We expressed the number of graphs with a fixed directed cycle double cover as the Gaussian matrix integral of an Ihara-Selberg-type function.


Papers submitted for publication

Publications in peer-reviewed journals

Extended abstracts in peer-reviewed conference proceedings

  • Amin Coja-Oghlan, Mihyun Kang, Lena Krieg, and Maurice Rolvien, The k-XORSAT threshold revisited, In Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications (EuroComb'23), 298-304.

  • Joshua Erde, Mihyun Kang, Florian Lehner, Bojan Mohar, and Dominik Schmid, Cop number of random k-uniform hypergraphs, In Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications (EuroComb'23), 416-424.

  • Amin Coja-Oghlan, Oliver Cooley, Mihyun Kang, Joon Lee, Jean Bernoulli Ravelomanana, The sparse parity matrix, In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA 2022), 822-833.

  • Oliver Cooley, Mihyun Kang, and Oleg Pikhurko, On a question of Vera T. Sos about size forcing of graphons (extended abstract), In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives, Springer.

  • Oliver Cooley, Mihyun Kang, and Julian Zalla, Loose cores and cycles in random hypergraphs (extended abstract), In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives, Springer.

  • Tuan Anh Do, Joshua Erde, and Mihyun Kang , Component behaviour of random bipartite graphs, In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives, Springer.

  • Chris Dowden, Mihyun Kang, Mirjana Mikalacki, and Milos Stojakovic, The game of Toucher and Isolator, In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives, Springer.

  • Mihyun Kang and Michael Missethan, Cut vertices in random planar graphs, In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2021), CRM Research Perspectives, Springer.

  • Mihyun Kang and Michael Missethan, The giant component and 2-core in sparse random outerplanar graphs, In Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Leibniz International Proceedings in Informatics 159 (2020), pp. 4:1-4:17. https://doi.org/10.4230/LIPIcs.AofA.2020.18. arxiv.org/abs/2004.13319.

  • Jason Gao and Mihyun Kang, Counting cubic maps with large genus, In Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Leibniz International Proceedings in Informatics 159 (2020), pp. 3:1-3:14. https://doi.org/10.4230/LIPIcs.AofA.2020.13.

  • Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel, Cohomology groups of non-uniform random simplicial complexes, In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019), Acta Math. Univ. Comenianae Vol. LXXXVIII, 3 (2019), pp. 553-560. http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1288/693.

  • Chris Dowden, Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel, The evolution of random graphs on surfaces of non-constant genus, In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019), Acta Math. Univ. Comenianae Vol. LXXXVIII, 3 (2019), pp. 631-636. http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1206.

  • Oliver Cooley, Wenjie Fang, Nicola Del Giudice, and Mihyun Kang, Subcritical random hypergraphs, high-order components, and hypertrees, In Proceedings of Analytic Algorithmics and Combinatorics (ANALCO), SIAM 2019, pp. 111-118. https://doi.org/10.1137/1.9781611975505.12.

  • Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel, Vanishing of cohomology groups of random simplicial complexes, In Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), Leibniz International Proceedings in Informatics 110 (2018), pp. 7:1-7:14. https://doi.org/10.4230/LIPIcs.AofA.2018.7.

  • Chris Dowden, Mihyun Kang, and Michael Krivelevich, The genus of the Erdos-Renyi random graph and the fragile genus property, In Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), Leibniz International Proceedings in Informatics 110 (2018), pp. 17:1-17:13. https://doi.org/10.4230/LIPIcs.AofA.2018.17.

  • Hsien-Kuei Hwang, Mihyun Kang, and Guan-Huei Duh, Asymptotic expansions for sub-critical Lagrangean forms, In Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), Leibniz International Proceedings in Informatics 110 (2018), pp. 29:1-29:13. https://doi.org/10.4230/LIPIcs.AofA.2018.29.

  • Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari, Mihyun Kang, and Tobias Kapetanopoulos, Charting the replica symmetric phase. In Proceedings of the 21th International Workshop on Randomization and Computation (RANDOM 2017), Leibniz International Proceedings in Informatics 81 (2017), pp. 40:1-40:17. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2017.40.

  • Chris Dowden, Mihyun Kang, and Philipp Sprüssel, The evolution of random graphs on surfaces. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics 61 (2017), pp. 367-373. https://doi.org/10.1016/j.endm.2017.06.061.

  • Oliver Cooley, Penny Haxell, Mihyun Kang, and Philipp Sprüssel, Homological connectedness of random hypergraphs. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics 61 (2017), pp. 279-285. https://doi.org/10.1016/j.endm.2017.06.049.

  • Mihyun Kang, Tamas Makai, and Oleg Pikhurko, Supersaturation Problem for the Bowtie. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics 61 (2017), pp. 679-685. https://doi.org/10.1016/j.endm.2017.07.023.

  • Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel, Evolution of the giant component in graphs on orientable surfaces. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics 61 (2017), pp. 687-693. https://doi.org/10.1016/j.endm.2017.07.024.

  • Mihyun Kang and Tamas Makai, Bootstrap percolation on G(n,p) revisited. In Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2016), pp. 1-12. http://arxiv.org/pdf/1605.02995v1.pdf.

  • Amin Coja-Oghlan, Oliver Cooley, Mihyun Kang, and Kathrin Skubch, The minimum bisection in the planted bisection model. In Proceedings of the 19th International Workshop on Randomization and Computation (RANDOM 2015), Leibniz International Proceedings in Informatics 40 (2015), pp. 710-725. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2015.710.

  • Mihyun Kang and Philipp Sprüssel, Charaterisation of symmetries of unlabelled triangulations. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics (2015), pp.587-594. https://doi.org/10.1016/j.endm.2015.06.080.

  • Wenjie Fang, Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel, Enumeration of cubic multigraphs on orientable surfaces. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics (2015), pp. 603-610. https://doi.org/10.1016/j.endm.2015.06.082.

  • Amin Coja-Oghlan, Oliver Cooley, Mihyun Kang, and Kathrin Skubch, How does the core sit inside the mantle?. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics (2015), pp. 489-496. https://doi.org/10.1016/j.endm.2015.06.068.

  • Mihyun Kang, Christoph Koch, and Tamas Makai, Bootstrap percolation in random k-uniform hypergraphs. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics (2015), pp. 595-601. https://doi.org/10.1016/j.endm.2015.06.081.

  • Oliver Cooley, Mihyun Kang, and Christoph Koch, Evolution of high-order connected components in random hypergraphs. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), Electronic Notes in Discrete Mathematics (2015), pp. 569-575. https://doi.org/10.1016/j.endm.2015.06.077.

  • Mihyun Kang, Angelica Pachon, and Pablo Rodriguez, Connectivity for a modified binomial random graph by agglomeration. In Proceedings of the 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2014), DMTCS proc. BA, 2014, pp. 217-228.

  • Andrea Jiménez, Mihyun Kang, and Martin Loebl, Directed cycle double covers: hexagon graphs. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), CRM Series 16 (2013), pp. 147-151.

  • Michael Behrisch, Amin Coja-Oghlan, and Mihyun Kang, Local Limit Theorems for the Giant Component of Random Hypergraphs. In Proceedings of the 11th International Workshop on Randomization and Computation (RANDOM 2007), LNCS 4627, pp. 341-352, 2007, Springer Verlag.

  • Noga Alon, Amin Coja-Oghlan, Hiêp Hàn, Mihyun Kang, Vojtěch Rödl, and Mathias Schacht, Quasi-randomness and algorithmic regularity for graphs with general degree distributions. In Proceedings of the 34th International Colloquium on Automata, Languages and Programmnig (ICALP 2007), LNCS 4596, 2007, pp. 789-800, Springer Verlag.

  • Manuel Bodirsky, Éric Fusy, Mihyun Kang, and Stefan Vigerske, An unbiased pointing operator for unlabeled structures, with applications to counting and sampling. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 356-365, 2007, ACM.

  • Mihyun Kang, Evolution of random graph processes with degree constraints. In Proceedings of the Sixth Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications (2006). Electronic Notes in Discrete Mathematics 28 (2007), pp. 493-500.

  • Manuel Bodirsky, Omer Giménez, Mihyun Kang, and Marc Noy, On the number of series-parallel and outerplanar graphs. In Proceedings of European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), DMTCS Proceedings Series, 2005, pp. 383-388.

  • Manuel Bodirsky, Clemens Gröpl, and Mihyun Kang, Sampling unlabeled biconnected planar graphs. In Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005), LNCS 3827, pp. 593-603, 2005, Springer Verlag.

  • Manuel Bodirsky, Clemens Gröpl, and Mihyun kang, Generating labeled planar graphs uniformly at random. In Proceedings of the Thirtieth International Colloquium on Automata, Languages and Programming (ICALP 2003), LNCS 2719, pp. 1095-1107, 2003, Springer Verlag.

  • Manuel Bodirsky, Clemens Gröpl, and Mihyun kang, Decomposing, counting and generating unlabeled cubic planar graphs uniformly at random. In Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb), ITI Series 2003-145, pp. 61-66, 2003.

Miscellaneous


Outreach articles

last updated in April 2024