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Discrete mathematics

Activity of the research group:

Fundamental research in graph theory, hypergraphs, combinatorics, combinatorial optimization, combinatorial number theory, game theory, database theory, rigidity of graphs and structures, additive combinatorics, combinatorial geometry, search theory, extremal set systems, relation between databases and code theory, graph coloring, behaviour of graph parameters in product graphs

Recent results:

Péter Pach Pál developed a new version of the polynomial method in 2016 together with Croot and Lev. This new method has led to the solution of famous problems such as the cap set problem or the Erdős-Szemerédi sunflower conjeture. Since then, the method has had many applications, such as exact bound for Green’s lemma of “arithmetical triangle removal” (Fox-Lovász), Sárközy’s theorem for polynomials over finite bodies (Green), and many others. The article was published in the most prestigious mathematical journal, Annals of Mathematics, and Fields Medal-winning mathematicians Gowers, Tao, and other leading mathematicians such as Cameron and Kalai have also analyzed it on their blogs.

Géza Tóth, together with János Pach and Gábor Tardos, proved far-reaching generalizations of the Crossing Lemma to multigraphs under various natural conditions.

Gábor Wiener, together with Peter Dameschke and Azam Sheikh Muhammad, laid the combinatorial foundations of a new, practical and well-used strict group testing model, which was published in the Journal of Combinatorial Theory A, one of the leading combinatorial journals.

Gábor Simonyi, together with Gábor Tardos, gave a partial (complete in the 4-chromatic case) characterisation of the colour-critical edges of Schrijver graphs.

Gyula Katona and László Papp, in a joint work with Ervin Győri, gave lower and upper bounds on the optimal pebbling number of large grids.

Gyula Katona, with Kitti Varga, achieved several significant results in the study of minimally tough graphs.

Recent projects:

MTA Lendület • OTKA

International relations:

Ibaraki University, Japan • Lancaster University, UK • University of Haifa, Israel • University of Warwick, UK • Ghent University • Yokohama National University • University of British Columbia, Canada • Sapienza – Universitá di Roma

Industrial partners:

Morgan Stanley • Lynx Analytics