[1][3] In 2018, Kráľ moved back to the Czech Republic and started working at Faculty of Informatics, Masaryk University, accepting the Donald Knuth professorship chair.
[4][5][6] In the 1970s, Michael D. Plummer and László Lovász conjectured that every bridgeless cubic graph has an exponential number of perfect matchings, strengthening Petersen's theorem that at least one perfect matching exists.
In a pair of papers with different sets of co-authors, Kráľ was able to show that this conjecture is true.
[7][8] Kráľ won first place and a gold medal at the International Olympiad in Informatics in 1996.
[11] He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to extremal combinatorics and graph theory, and for service to the profession".