mathematics

Zdeněk Dvořák

Zdeněk Dvořák is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Zdeněk Dvořák rather than just read about it. In short: Zdeněk Dvořák (born April 26, 1981) is a Czech mathematician specializing in graph theory. Dvořák was born in Nové Město na Moravě.

Key takeaways

Zdeněk Dvořák belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Zdeněk Dvořák to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Zdeněk Dvořák from memory before moving on to harder problems.

Reference excerpt

Zdeněk Dvořák (born April 26, 1981) is a Czech mathematician specializing in graph theory. Dvořák was born in Nové Město na Moravě. He competed on the Czech national team in the 1999 International Mathematical Olympiad, and in the same year in the International Olympiad in Informatics, where he won a gold medal. He earned his Ph.D. in 2007 from Charles University in Prague, under the supervision of Jaroslav Nešetřil. He remained as a research fellow at Charles University until 2010, and then did postdoctoral studies at the Georgia Institute of Technology and Simon Fraser University. He then returned to the Computer Science Institute (IUUK) of Charles University, obtained his habilitation in 2012, and has been a full professor there since 2022. He was one of three winners of the 2015 European Prize in Combinatorics, "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. It states that there exists a constant d such that, if a planar graph has no two triangles within distance d of each other, then it can be colored 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 conjectured in 2001 that triangle-free graphs of maximum degree three have fractional chromatic number 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 Home page

Worked examples

Example 1 — a first encounter with Zdeněk Dvořák

Start with the simplest possible case. Write down what Zdeněk Dvořák claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Zdeněk Dvořák before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Zdeněk Dvořák ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Zdeněk Dvořák

In research: Zdeněk Dvořák appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Zdeněk Dvořák in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Zdeněk Dvořák is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1981 births, 21st-century mathematicians, Academic staff of Charles University, so understanding it makes those chapters shorter.
In everyday life: Look for Zdeněk Dvořák outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Zdeněk Dvořák in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Zdeněk Dvořák means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Zdeněk Dvořák out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Zdeněk Dvořák in simple terms?

Zdeněk Dvořák (born April 26, 1981) is a Czech mathematician specializing in graph theory. Dvořák was born in Nové Město na Moravě.

Why does Zdeněk Dvořák matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Zdeněk Dvořák?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Zdeněk Dvořák.