Combinatorial group

Here you can find the outputs of the project *Random Discrete Structures*, project number GJ20-27757Y, funded by the Czech Science foundation. For other outputs, please visit this page. In bold you find the authors that were supported by the grant.

## Preprints

Ramsey numbers of cycles in random graphs, **P. Araújo**, Matías Pavez-Signé, Nicolás Sanhueza-Matamala

Prominent examples of flip processes, **P. Araújo**, J. Hladký, E. K. Hng, **M. Šileikis**

Deviation probabilities for arithmetic progressions and irregular discrete structures, S. Griffiths, C. Koch, **M. Secco**

On the anti-Ramsey threshold for non-balanced graphs, **P. Araújo**, T. Martins, L. Mattos, W. Mendonça, L. Moreira, and G. O. Mota

## Conference papers

On the Intersections of Non-homotopic Loops, V. Blažej, M. Opler, **M. Šileikis**, P. Valtr (2021), * In: Mudgal A., Subramanian C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science, vol 12601. Springer, Cham. * First Online: 28 January 2021.

Non-homotopic Loops with a Bounded Number of Pairwise Intersections, V. Blažej, M. Opler, **M. Šileikis**, P. Valtr (2021), *Proceedings of the 29th International Symposium on Graph Drawing and Network Visualization (GD 2021), LNCS 12868 (pp. 210-222). Springer, Cham.* Preprint. First Online: 23 December 2021.

## Accepted journal papers

From flip processes to dynamical systems on graphons, F. Garbe, J. Hladký, **M. Šileikis**, F. Skerman, accepted to *Annales de l'Institut Henri Poincaré, Series B*

## Published journal papers

Ramsey goodness of trees in random graphs, **P. Araújo**, Luiz Moreira, and Matı́as Pavez-Signé, accepted to *Random Structures & Algorithms* (2022+), early view

Sandwiching biregular random graphs, T. Klimošová, C. Reiher, A. Ruciński, **M. Šileikis**, *Combinatorics, Probability and Computing* 32-1, pp. 1-44 (2023)

## Journal papers revised during the project

Upper tail bounds for Stars, **M. Šileikis**, L. Warnke, *The Electronic Journal of Combinatorics*, Volume 27, Issue 1 (2020)

A limit theorem for small cliques in inhomogeneous random graphs, J. Hladký, C. Pelekis, **M. Šileikis**, *Journal of Graph Theory*, 97-4, pp. 578-599 (2021)

Counting extensions revisited, **M. Šileikis**, L. Warnke, *Random Structures & Algorithms, *Volume 61, Issue 1, pp. 3-30 (2022), DOI:10.1002/rsa.21050