Prof. Daniel Kráľ is an internationally recognized researcher in combinatorics and graph theory. In addition to the algorithmic questions, that are the topic of this presentation, he studies structural graph theory, in particular graph colorings, extremal combinatorics, and combinatorial limits. He has published more than 100 journal papers, including ones in top journals Advances in Mathematics, Geometric and Functional Analysis, and Journal of the ACM. He also has numerous publications in the top selective theoretical computer science conferences including FOCS, SODA, ICALP. He was the first member of Czech computer science community who received ERC grant (starting grant). Other awards include the European Prize in Combinatorics and Bolzano Award, he was the absolute winner of the International Olympiad in Informatics (one of only two Czech absolute winners in the history). Except for Charles University in Prague he held positions at Georgia Inst. of Technology and TU Berlin; currently he is a professor at Univ. of Warwick and a member of the center DIMAP there.