Extremal and Probabilistic Combinatorics GAČR project

EPC – Extremal and Probabilistic Combinatorics – is a 5-year project from January 1, 2023 to December 31, 2027 at Czech Technical University in Prague supported by Czech Science Foundation.

Team members (ordered by the starting date):

List of research outputs supported by the project:

Balogh, Clemen, Lidický, Norin, Volec: The Spectrum of Triangle-Free Graphs, SIAM Journal on Discrete Mathematics 37 (2023), 1173-1179.
Trödler, Volec, Vybíral: A tight lower bound on the minimal dispersion, European Journal of Combinatorics 120 (2024), article no. 103945, 5pp.
Kráľ, Volec, Wei: Common graphs with arbitrary chromatic number, Compos. Math. 161 (2025), 594-634.
Trödler, Volec, Vybíral: Lower bounds on the minimal dispersion of point sets via cover-free families, Journal of Complexity 91 (2025), article no. 101974, 7pp. Extended Abstract accepted to Eurocomb 2025.
Grzesik, Rödl, Volec: Subgraphs with a positive minimum semidegree in digraphs with large outdegree, Innovations in Graph Theory 2 (2025), 301-312.
Lang, Schacht, Volec: Tight Hamiltonicity from dense links of triples, submitted.
Černá, Kielak, Volec: On Shattering Triples with Six Permutations, Extended Abstract accepted to Eurocomb 2025.
Balogh, Lidický, Mubayi, Pfender, Volec: Semi-Inducibility of some small graphs, submitted.
Kráľ, Krnc, Kučerák, Lidický, Volec: Sidorenko property and forcing in regular tournaments, submitted.

List of presentations supported by the project:

January 16, 2023: DIMAP seminar, University of Warwick
April 13, 2023: Discrete Mathematics seminar, KIT
May 2, 2023: Graph Theory Seminar, West Bohemia University
May 15 - May 19, 2023: Series of lectures at Flag Algebras Summer School 2023 hosted by Iowa State University
June 13, 2023: Graph Theory and Combinatorics Workshop at FoCM 2023 – 6th diagonal Ramsey number is at most 147
September 4, 2023: 31st Workshop Cycles and Colourings – Common graphs with arbitrary chromatic number
November 17, 2023: Research Seminar Combinatorics, FU Berlin
February 9, 2024: KdVI Discrete Mathematics Seminar, University of Amsterdam
March 8, 2024: Extremal graph theory seminar, Czech Academy of Sciences
April 9, 2024: G²OAT seminar, FIT CTU – Subgraphs with a positive minimum semidegree in digraphs with large outdegree
June 7, 2024: Statistics seminar, University of Sherbrooke
July 4, 2024: 30th British Combinatorial Conference – Subgraphs with a positive minimum semidegree in digraphs with large outdegree
July 17, 2024: 9th European Congress of Mathematics (Extremal and probabilistic combinatorics mini-symposium) – The 6th diagonal Ramsey number
May 12, 2025: G²OAT seminar, FIT CTU – Shattering triples with six permutations
May 20, 2025: 10th Canadian Discrete and Algorithmic Mathematics Conference (Interdisciplinary Extremal Combinatorics mini-symposium) – Minimum dispersion of point sets
July 24, 2025: 2025 International Conference on Continuous Optimization (SDPs and their applications across mathematics session) – Shattering triples with permutations
August 7, 2025: 22nd International Conference on Random Structures and Algorithms – Flag algebras for fixed-size structures
August 20, 2025: 2025 Koper-Leipzig Graph Theory Workshop – The Flag Algebra Method
August 25, 2025: 13th European Conference on Combinatorics, Graph Theory and Applications – On Shattering Triples with Six Permutations
August 29, 2025: 13th European Conference on Combinatorics, Graph Theory and Applications – Lower bounds on the minimal dispersion of point sets via cover-free families
September 17, 2025: School on Theoretical Informatics, Graphs And Mathematical Applications 2025 – Combinatorial inequalities and applications to dispersion
September 18, 2025: School on Theoretical Informatics, Graphs And Mathematical Applications 2025 – Shattering Triples with Six Permutations and related problems
October 6, 2025: Seminar on Foundations of Computing, FI MUNI – Shattering triples with six permutations and related problems
October 17, 2025: Flag algebras and extremal combinatorics Workshop at American Institute of Mathematics – Some stories from using flag algebras (Tips & Tricks)

A brief project log – 2023:

January 2023: Revision of the submission The Spectrum of Triangle-Free Graphs (arxiv:2204.00093v3) – creating a verification script for the computer-generated part of the proof of the main theorem
January 2023: Research visit of Jan to the group of Oleg Pikhurko (Warwick)
February 2023: Reserach visit of Jing Guo (MSc student at ALGANT program, Regensburg/Bordeaux) to our group
March 2023: Research visit of Andrzej Grzesik (JU Kraków) and Magdalena Prorok (PhD student, AGH Kraków) to our group
April 2023: Research visits of Jan to Jean-Sébastien Sereni (Strasbourg) and Felix Clemen (KIT)
May 2023: Research visit of Jan to Bernard Lidický (IA State)
June 2023: Research visit of David Munhá Correia (ETH Zürich) to our group
June 2023: The Spectrum of Triangle-Free Graphs gets published in SIDMA
July 2023: Pedro Araújo joins the team as the very first postdoc
September 2023: Research visit of Jan to Andrzej Grzesik (JU Kraków)
October 2023: Jan's participation at SQuaRE Collaboration Workshop at American Institute of Mathematics
November 2023: Research visit of Jan to the group of Tibor Szabó (FU Berlin) and Christoph Spiegel (Zuse Institute Berlin)
November 2023: Submission of A tight lower bound on the minimal dispersion (arXiv:2311.10666)

A brief project log – 2024:

January 2024: Revision of the submission Common graphs with arbitrary chromatic number (arxiv:2206.05800v3)
January 2024: Research visit of Jan to Mathias Schacht and Richard Lang (both U. Hamburg)
February 2024: Research visit of Jan to the group of Ross Kang (U. of Amsterdam)
March 2024: A tight lower bound on the minimal dispersion gets published in EuJC
March 2024: Submission of Tight Hamiltonicity from dense links of triples (arxiv:2403.14518)
March 2024: Research visit of Jan to the group of Ross Kang (U. of Amsterdam)
May 2024: Research visit of Andrzej Grzesik (JU Kraków) to our group
May-August 2024: Research visit of Vojta Rödl (Emory) to our group
June 2024: Research visits of Jan to Sergey Norin and Louigi Addario-Berry (both McGill), Klaus Hermann (U. of Sherbrooke), and Alex Scott (Oxford)
June 2024: Research visit of Pedro to Leticia Mattos (Heidelberg U.)
June 2024: Daniela Opočenská joins the team as a PhD student
July 2024: Research visit of Bernard Lidický (IA State) to our group
August 2024: Submission of Subgraphs with a positive minimum semidegree in digraphs with large outdegree (arxiv:2408.06015)
October 2024: Jan's participation at SQuaRE Collaboration Workshop at American Institute of Mathematics
November and December 2024: preparation for grant transfer to Faculty of Information Technology (FIT)

A brief project log – 2025:

January 2025: the grant was successfully transferred to Faculty of Information Technology (FIT)
January to April 2025: Research visit of Bartek Kielak to our group
January and February 2025: Research visit of Jan to Bernard Lidický, Flo Pfender, Matija Bucic, Dan Kráľ and Mathias Schacht (all SLMath)
January to March 2025: Research visit of Pedro to Luiz Moreira (Universidade Federal de Pernambuco) and Lucas Aragão (Universidade do Estado do Rio de Janeiro)
February 2025: Alexander Clifton joins the team as a postdoc
April 2025: Submission of Lower bounds on the minimal dispersion of point sets via cover-free families (arxiv:2504.00715)
April 2025: Pedro leaves the team and starts a tenure-track job at UFPE (Brazil)
May 2025: Acceptance of Eurocomb submission – On Shattering Triples with Six Permutations
May 2025: Acceptance of Eurocomb submission – Lower bounds on the minimal dispersion of point sets via cover-free families
May 2025: Research visit of Jan to McGill
June 2025: Research visit of Daniela to IA State
June 2025: Lower bounds on the minimal dispersion of point sets via cover-free families gets published in Journal of Complexity
June and July 2025: Research visit of Ayush Basu and Vojta Rödl (both Emory) to our group
July 2025: Common graphs with arbitrary chromatic number gets published in Compositio Mathematica
July 2025: Revision of the submission Tight Hamiltonicity from dense links of triples (arxiv:2403.14518v2) – main argument reworked
August 2025: Research visit of Alexander and Jan to Matjaž Krnc and Martin Milanič (both Univerza na Primorskem)
September 2025: Research visit of Daniela to Matjaž Krnc (Univerza na Primorskem)
October 2025: Robert Hancock joins the team as a postdoc
October 2025: Research visit of Jan to Bernard Lidický (IA State)
October 2025: Jan's participation at Flag algebras and extremal combinatorics Workshop at American Institute of Mathematics
November 2025: Subgraphs with a positive minimum semidegree in digraphs with large outdegree gets published in Innovations in Graph Theory
December 2025: Research visit of Jan to the group of Ross Kang (U. of Amsterdam)

Extremal and Probabilistic Combinatorics (GAČR 23-06815M)