Zdeněk Dvořák (born April 26, 1981) is a Czech mathematician specializing in

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

. Dvořák was born in

Nové Město na Moravě Nové Město na Moravě (; ) is a town in Žďár nad Sázavou District in the Vysočina Region of the Czech Republic. It has about 9,800 inhabitants. It is known as a winter sports resort. The historic town centre is well preserved and is protecte ...

. He competed on the Czech national team in the 1999

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

, and in the same year in the

International Olympiad in Informatics The International Olympiad in Informatics (IOI) is an annual competitive programming competition and one of the International Science Olympiads Student competition, for secondary school students. The first IOI was held in 1989 in Pravetz, Bulgar ...

, where he won a gold medal. He earned his Ph.D. in 2007 from

Charles University in Prague Charles University (CUNI; , UK; ; ), or historically as the University of Prague (), is the largest university in the Czech Republic. It is one of the oldest universities in the world in continuous operation, the oldest university north of the ...

, under the supervision of

Jaroslav Nešetřil Jaroslav Nešetřil (; born 13 March 1946) is a Czech mathematician. His research areas include combinatorics (structural combinatorics, Ramsey theory), graph theory (coloring problems, sparse structures), algebra (representation of structures, c ...

. He remained as a research fellow at Charles University until 2010, and then did postdoctoral studies at the

Georgia Institute of Technology The Georgia Institute of Technology (commonly referred to as Georgia Tech, GT, and simply Tech or the Institute) is a public university, public research university and Institute of technology (United States), institute of technology in Atlanta, ...

and

Simon Fraser University Simon Fraser University (SFU) is a Public university, public research university in British Columbia, Canada. It maintains three campuses in Greater Vancouver, respectively located in Burnaby (main campus), Surrey, British Columbia, Surrey, and ...

. He then returned to the Computer Science Institute (IUUK) of Charles University, obtained his

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...

in 2012, and has been a full professor there since 2022.. He was one of three winners of the 2015

European Prize in Combinatorics The European Prize in Combinatorics is a prize for research in combinatorics, a mathematical discipline, which is awarded biennially at Eurocomb, the European conference on combinatorics, graph theory, and applications.. The prize was first awarde ...

, "for his fundamental contributions to graph theory, in particular for his work on structural aspects of graph theory, including solutions to Havel's 1969 problem and the Heckman–Thomas 14/5 problem on fractional colourings of cubic triangle-free graphs. This refers to two different results of Dvořák: *Havel's conjecture is a strengthening of

Grötzsch's theorem In the mathematics, mathematical field of graph theory, Grötzsch's theorem is the statement that every triangle-free graph, triangle-free planar graph can be graph coloring, colored with only three colors. According to the four-color theorem, eve ...

. It states that there exists a constant ''d'' such that, if a

planar graph In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. ...

has no two triangles within distance ''d'' of each other, then it can be

colored ''Colored'' (or ''coloured'') is a racial descriptor historically used in the United States during the Jim Crow era to refer to an African American. In many places, it may be considered a slur. Dictionary definitions The word ''colored'' wa ...

with three colors. A proof of this conjecture of Havel was announced by Dvořák and his co-authors in 2009. *C. C. Heckman and

Robin Thomas Robin Thomas is an American film, television and theater actor, and sculptor. Career Thomas' best-known television roles are as Mark Singleton on '' Another World'' (1983–85), and as Geoffrey Wells on ''Who's the Boss?''. He also portrayed ...

conjectured in 2001 that

triangle-free graph In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with ...

s of maximum degree three have

fractional chromatic number Fractional coloring is a topic in a branch of graph theory known as fractional graph theory. It is a generalization of ordinary graph coloring. In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices ...

at most 14/5. A proof was announced by Dvořák and his co-authors in 2013 and published by them in 2014..

References

External links

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{{DEFAULTSORT:Dvorak, Zdenek 1981 births Living people Czech mathematicians Graph theorists Charles University alumni Academic staff of Charles University