Warwick University campus Prague Castle and Charles Bridge Petrov hill in Brno


Basic info

My name is Daniel Kráľ. I have recently moved to the Faculty of Informatics of Masaryk University in Brno, Czech Republic, where I have been the inaugural holder of the newly established Donald Ervin Knuth Professorship, which the university has created with the permission of Donald Knuth. I am co-heading the Laboratory of Discrete Methods and Algorithms (DIMEA) of the Faculty. I am also honorary professor at the University of Warwick, where, before moving to Brno, I was a professor of mathematics and computer science at the University of Warwick and was also affiliated its research centre DIMAP.

My research work concerns graph theory and related fields in mathematics and computer science. Most of my research is now focused on topics related to my ERC Consolidator grant LADIST, which builds on the ERC Starting grant CCOSA.

Contact details

E-mail: dkral -at- fi.muni.cz
Office: C517, main FI building

Teaching in the academic year 2020/21

MA010 Graph Theory

Advances in Combinatorics

Advances in Combinatorics is an overlay combinatorial journal, which follows a model established by the journal Discrete Analysis for diamond open access. The journal aims to be a diamond open access journal at the level of the very top combinatorial journals. It has no printed copies; instead the journal provides links to the published versions of the articles on arXiv. After the lanuch in June 2018, the first five papers were published in October 2019. The journal is a part of the Free Journal Network and has been accepted to be indexed by Scopus.

The journal has received over 80 submissions and continues welcoming submissions containing high quality results in combinatorics; the average decision time (excluding desk rejects) is 8.5 months (as of August 2020). The editorial board consists of Béla Bollobás, Reinhard Diestel, Timothy Gowers, Dan Král', Daniela Kühn, James Oxley, Bruce Reed, Gábor Sárközy, Asaf Shapira and Robin Thomas, with Tim and myself also acting as the managing editors. The financial and administrative support for the journal is provided by Queen's University Library.

Additional information on the aims of the journal and ethical publishing in general can be found in this blog post and this blog post by Tim Gowers.

Recent and future co-organized events

Research interests

My research addresses several topics in mathematics, computer science and their interface. I am primarily interested in problems concerning structural and extremal graph theory, graph algorithms and graph limits. In particular, the theory of graph limits is a new area of mathematics which provides analytic tools to study large graphs, e.g., graphs representing social networks. These analytic methods have also led to new ways to deal with notoriously difficult extremal combinatorics questions and established new links between analysis, combinatorics, ergodic theory, group theory and probability theory.

Further details, including a short introduction accessible to non-specialists, can be found here.