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Research Grant ``Asymptotic properties of graphs on a surface''
Summary
Since the foundation of the theory of random graphs by Erdos and Renyi five decades ago, various random graphs have been introduced and studied. One example is random graphs on a surface, in particular random planar graphs. Graphs on a 2dimensional surface and related objects (e.g. planar graphs, triangulations) have been among the most studied objects in graph theory, enumerative combinatorics, discrete probability theory, and statistical physics. The main objectives of this project are to study the asymptotic properties and limit behaviour of random graphs on a surface (e.g. evolution, phase transition, critical behaviour, component size distribution) and to investigate enumerative and algorithmic aspects of unlabelled graphs on a surface (e.g. connectivity, symmetry, decomposition, random generation).
Grant Info
Supported by Austrian Science Fund (FWF), Grant no. P27290, 01.06.201530.06.2019
Team
 Oliver Cooley
 Chris Dowden
 Wenjie Fang
 Mihyun Kang (PI)
 Michael Moßhammer (PhD defence on May 4, 2018)
 Philipp Sprüssel (CoPI)
Collaborators and visitors
 Ron Aharoni, Technion
 Michael Drmota, TU Wien
 Eric Fusy, Ecole Polytechnique
 Daniele Gardy, Universite de Versailles SaintQuentin
 Jason Zhicheng Gao, Carleton University
 Mikhail Isaev, Monash University
 Michael Krievelevich, Tel Aviv University
 Colin McDiarmid, University of Oxford
 Konstantinos Panagiotou, University of Munich
 Milos Stojakovic, University of Novi Sad
Publications
Articles in Journals
 Oliver Cooley, Wenjie Fang, Nicola Del Giudice, and Mihyun Kang,
Subcritical random hypergraphs, highorder components, and hypertrees,
SIAM Journal on Discrete Mathematics 34 (2020), 20332062, https://doi.org/10.1137/18M1221527 .
 Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel, Phase transitions in graphs on orientable surfaces, Random Structures and Algorithms (2019), 154. https://doi.org/10.1002/rsa.20900.
 Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philpp Sprüssel,
Vanishing of cohomology groups of random simplicial complexes,
Random Structures and Algorithms 56 (2020), 461500, https://doi.org/10.1002/rsa.20857.
 Chris Dowden, Mihyun Kang, and Michael Krivelevich,
The genus of the ErdosRenyi random graph and the fragile genus property,
Random Structures and Algorithms 56 (2020), 97121, https://doi.org/10.1002/rsa.20871.
 Chris Dowden, Mihyun Kang, Mirjana Mikalacki, and Milos Stojakovic, The ToucherIsolator game, Electronic Journal of Combinatorics (2019), #P4.6.
 Mihyun Kang and Philipp Sprüssel, Symmetries of unlabelled planar triangulations, Electronic Journal of Combinatorics 25 (2018), #P1.34.
 Wenjie Fang, Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel, Cubic graphs and related triangulations on orientable surfaces, Electronic Journal of Combinatorics 25 (2018), #P1.30.
 Chris Dowden, Mihyun Kang, and Philipp Sprüssel, The evolution of random graphs on surfaces, SIAM Journal on Discrete Mathematics 32 (2018), 695727.
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.
 Chris Dowden, Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel,
The evolution of random graphs on surfaces of nonconstant genus, In the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2019), Acta Math. Univ. Comenianae
Vol. LXXXVIII, 3 (2019), pp. 631636.
 Oliver Cooley, Wenjie Fang, Nicola Del Giudice, and Mihyun Kang, Subcritical random hypergraphs, highorder components, and hypertrees, In Proceedings of Analytic Algorithmics and Combinatorics (ANALCO19), pp. 111118, https://doi.org/10.1137/1.9781611975505.12.
 Oliver Cooley, Nicola Del Giudice, Mihyun Kang, and Philipp Sprü:ssel, Vanishing of cohomology groups of random simplicial complexes,
In the Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), pp. 7:17:14, doi:10.4230/LIPIcs.AofA.2018.7.
 Chris Dowden, Mihyun Kang, and Michael Krivelevich, The genus of the ErdosRenyi random graph and the fragile genus property,
In the Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), pp. 17:117:13, doi:10.4230/LIPIcs.AofA.2018.17.
In the Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018).
 Chris Dowden, Mihyun Kang, and Philipp Sprussel,
The evolution of random graphs on surfaces.
In the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2017), Electronic Notes in Discrete Mathematics 61 (2017), pp. 367373.
 Oliver Cooley, Penny Haxell, Mihyun Kang, and Philipp SprÃ¼ssel,
Homological connectedness of random hypergraphs.
In the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2017), Electronic Notes in Discrete Mathematics 61 (2017), pp. 279285.
 Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel,
Evolution of the giant component in graphs on orientable surfaces,
In the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2017), Electronic Notes in Discrete Mathematics 61 (2017), pp. 687693.
 Mihyun Kang and Philipp Sprüssel,
Charaterisation of symmetries of unlabelled triangulations,
In the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2015), Electronic Notes in Discrete Mathematics (2015), pp.587594.
 Wenjie Fang, Mihyun Kang, Michael Moßhammer, and Philipp Sprüssel,
Enumeration of cubic multigraphs on orientable surfaces,
In the Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2015), Electronic Notes in Discrete Mathematics (2015), pp. 603610.
Thesis
 Michael Moßhammer, Phase transitions and structural properties of random graphs on surfaces, PhD Thesis, May 2018.
last updated in January 2020
