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Combinatorics Group
Research Grant ``Random Graphs: Cores, Colourings and Contagion''
Summary
The aim of this collaborative project, which is hosted jointly at Goethe University Frankfurt in Germany and at TU Graz in Austria, is to advance the rigorous mathematical understanding of random graphs with the assistance of novel mathematical tools originating, for example, from enumerative combinatorics or the recent theory of graph limits. Specific problems that we intend to study include the graph colouring problem on random graphs, strongly connected substructures of random graphs called cores and the contagion of cascading events. For example, graph colouring has been a core topic of mathematics since the famous four colour problem posed by Gutherie in 1852. Cores have applications, for example, in coding theory, and contagion is a key topic in the study of complex social or artificial networks.
Grant Info
 International Cooperation Project (DACH Scheme)
 Supported by Austrian Science Fund (FWF I3747) and German Research Foundation (DFG CO 646/4)
 Support period by FWF: 01.09.201830.06.2022
Team
 Goethe University Frankfurt
 Amin CojaOghlan (PI)
 Jean Bernoulli Ravelomanana (PhD student)
 TU Graz
 Oliver Cooley (postdoctoral research fellow)
 Mihyun Kang (PI)
Collaborators and visitors in Graz
 Amin CojaOghlan, Goethe University Frankfurt
 Nikolaos Fountoulakis, University of Birmingham
 Tobias Kapetanopoulos, Goethe University Frankfurt
 Jaehoon Kim, University of Warwick (KAIST since July 2019)
 Michael Krievelevich, Tel Aviv University
 Joon Lee, Goethe University Frankfurt
 Oleg Pikhurko, University of Warwick
 Jean Bernoulli Ravelomanana, Goethe University Frankfurt
 Benny Sudakov, ETH Zürich
Publications (supported by FWF I3747)
Articles in peerreviewed journals
 Oliver Cooley, Tobias Kapetanopoulos, and Tamas Makai, The sharp threshold for jigsaw percolation in random graphs, Advances in Applied Probability 51 (2019), 378407, doi:10.1017/apr.2019.24.
 Oliver Cooley and Abraham Gutierrez, Multicoloured jigsaw percolation on random graphs, Journal of Combinatorics 11 (2020), 603624, doi:10.4310/JOC.2020.v11.n4.a2.
 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), 11341156, doi:10.1002/rsa.20970.
 Joshua Erde, Mihyun Kang, and Michael Krivelevich,
Large complete minors in random subgraphs,
Combinatorics, Probability and Computing 30 (2021), 619630, doi:10.1017/S0963548320000607.
 Oliver Cooley, Nemanja Draganic, Mihyun Kang, and Benny Sudakov, Large induced matchings in random graphs, SIAM J. Discrete Math. 351 (2021), 267280, doi:10.1137/20M1330609.
 Oliver Cooley, Frederik Garbe, Eng Keat Hng, Mihyun Kang, Nicolas SanhuezaMatamala, and Julian Zalla,
Longest paths in random hypergraphs, accepted for publication in SIAM J. Discrete Math. (2021).
 Mihyun Kang and Michael Missethan, Longest and shortest cycles in random planar graphs, Random Structures and Algorithms (2021), 144, doi:10.1002/rsa.21040.
Articles in peerreviewed conference proceedings
 Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel, Cohomology groups of nonuniform random simplicial complexes, In the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019), Acta Math. Univ. Comenianae Vol. LXXXVIII, 3 (2019), pp. 553560.

Oliver Cooley, Mihyun Kang, and Oleg Pikhurko,
On a question of Vera T. Sos about size forcing of graphons (extended abstract),
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),
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.

Amin CojaOghlan, Oliver Cooley, Mihyun Kang, Joon Lee, Jean Bernoulli Ravelomanana,
The sparse parity matrix,
In Proceedings of the 2022 Annual ACMSIAM Symposium on Discrete Algorithms (SODA), pp. 822833.
doi:10.1137/1.9781611977073.35.
Articles submitted for publication
 Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprüssel,
Phase transition in cohomology groups of nonuniform random simplicial complexes.
 Oliver Cooley, Mihyun Kang, and Julian Zalla,
Loose cores and cycles in random hypergraphs.
 Oliver Cooley, Mihyun Kang, and Oleg Pikhurko, On a question of Vera T. Sós about size forcing of graphons.
 Amin CojaOghlan, Oliver Cooley, Mihyun Kang, Joon Lee, Jean Bernoulli Ravelomanana, The sparse parity matrix.
 Mikhail Isaev and Mihyun Kang, On the chromatic number in the stochastic block model.
 Mikhail Isaev and Mihyun Kang, On the chromatic number of graphons.
 Oliver Cooley, Joon Lee, Jean Bernoulli Ravelomanana, Warning Propagation: stability and subcriticality.
Thesis
Graz, December 2019
last updated in January 2022
