Project Graph limits and inhomogeneous random graphs
A "Junior project" Funded by the Czech Science Foundation for the period January 2018-June 2021, the project "Graph limits and inhomogeneous random graphs" aims to advance understanding of limits of discrete structures (and dense and sparse graph limits in particular) and related inhomogeneous random discrete structures. The project is hosted by the Institute of Mathematics of the Czech Academy of Sciences.
We have a vivid collaboration with the Extremal graph theory group at the Institute of Computer Science of the Czech Academy of Sciences.
Papers stemming from the project
- Ch. Pelekis: On the Shannon entropy of the number of vertices with zero in-degree in randomly oriented hypergraphs
Le Matematiche 74 (1), 2019, pp. 119-130; [published]; [arXiv]
- K. Engel, Th. Mitsis, Ch. Pelekis, Ch. Reiher: Projection inequalities for antichains
Israel Journal of Mathematics volume 238, pages 61-90(2020); [published]; [arXiv]
- M. Dolezal, Th. Mitsis, Ch. Pelekis: The de Bruijn-Erdos theorem from a Hausdorff measure point of view
Acta Mathematica Hungarica 159 (2), 2019, pp. 400-413; [published]; [arXiv]
- Th. Mitsis, Chr. Pelekis, V. Vlasak: A continuous analogue of Erdos' k-Sperner theorem
Journal of Mathematical Analysis and Applications, Volume 484, Issue 2 (2020), 123754; [published], [arXiv]
- C. Pelekis, V. Vlasak: On k-antichains in the unit n-cube
Publicationes Mathematica Debrecen, Volume 96, Issue 3-4 (2020), 15; [published]; [arXiv]
- M. Dolezal, J. Hladky, J. Kolar, T. Mitsis, C. Pelekis, V. Vlasak: A Turan-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems
accepted to Discrete & Computational Geometry; [published]; [arXiv]. [Here] is an identical copy of the published paper available as open access. [Extended abstract] appeared in the proceedings of Eurocomb 2019 [here]
- M. Dolezal, J. Grebik, J. Hladky, I. Rocha, V. Rozhon: Relating the cut distance and the weak* topology for graphons
accepted to Journal of Combinatorial Theory, series B; [published]; [arXiv]
- F. Garbe, J. Hladky, J. Lee: Two remarks on graph norms
accepted to Discrete & Computational Geometry, [arXiv], [published]
- J. Hladky, Ch. Pelekis, M. Sileikis: A limit theorem for small cliques in inhomogeneous random graphs
accepted to Journal of Graph Theory, [arXiv], [published]
- M. Dolezal: Graph limits: An alternative approach to s-graphons
accepted to Journal of Graph Theory, [arXiv]
- O. Cooley, F. Garbe, E. K. Hng, M. Kang, N. Sanhueza-Matamala, J. Zalla: Longest paths in random hypergraphs
accepted to SIAM Journal on Discrete Mathematics, [arXiv]
Density calculator allows to compute H-densities in step-graphons. Thanks to Frederik Garbe.
- F. Garbe, R. Hancock, J. Hladky, M. Sharifzadeh: Limits of Latin squares
[arXiv]; extended abstract
"Theory of limits of sequences of Latin squares"
appeared in proceedings of Eurocomb 2019 [here]
- R. Fokkink, L. Meester, C. Pelekis: Optimizing stakes in simultaneous bets
- M. Dolezal, J. Grebik, J. Hladky, I. Rocha, V. Rozhon: Cut distance identifying graphon parameters over weak* limits
Working with us
We have funds for short-term student/postdoc visits. Strong background in random graphs/random discrete structures/extremal graph theory is required. Please, contact us if you are interested.
The Institute of Mathematics has postdocs openings (typically with deadlines in March and September) within the "Academic Human Resource Programme" advertised. We would be happy to answer any questions a potantial candidate might have. Please, also contact us if you are considering joining the group using external funding, such as the Marie Sklodowska-Curie fellowship programme.