mathematics

Vadim G. Vizing

Vadim G. Vizing 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 Vadim G. Vizing rather than just read about it. In short: Vadim Georgievich Vizing (Russian: Вади́м Гео́ргиевич Визинг, Ukrainian: Вадим Георгійович Візінг; 25 March 1937 – 23 August 2017) was a Soviet and Ukrainian mathematician known for his contributions to graph theory, and especially for Vizing's theorem stating that the edges of any simple graph with maximum degree Δ can be colored with at most Δ + 1 colors. Biography Vizing was born in Kiev on March 25, 1937.

Key takeaways

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

Reference excerpt

Vadim Georgievich Vizing (Russian: Вади́м Гео́ргиевич Визинг, Ukrainian: Вадим Георгійович Візінг; 25 March 1937 – 23 August 2017) was a Soviet and Ukrainian mathematician known for his contributions to graph theory, and especially for Vizing's theorem stating that the edges of any simple graph with maximum degree Δ can be colored with at most Δ + 1 colors.

Biography Vizing was born in Kiev on March 25, 1937. His mother was half-German, and because of this the Soviet authorities forced his family to move to Siberia in 1947. After completing his undergraduate studies in mathematics in Tomsk State University in 1959, he began his Ph.D. studies at the Steklov Institute of Mathematics in Moscow, on the subject of function approximation, but he left in 1962 without completing his degree. Instead, he returned to Novosibirsk, working from 1962 to 1968 at the Russian Academy of Sciences there and earning a Ph.D. in 1966. In Novosibirsk, he was a regular participant in A. A. Zykov's seminar in graph theory. After holding various additional positions, he moved to Odessa in 1974, where he taught mathematics for many years at the Academy for Food Technology (originally known as Одесский технологический институт пищевой промышленности им. М. В. Ломоносова, "Odessa Technological Institute of Food Industry named after Mikhail Lomonosov").

Research results The result now known as Vizing's theorem, published in 1964, when Vizing was working in Novosibirsk, states that the edges of any graph with at most Δ edges per vertex can be colored using at most Δ + 1 colors.[V64] It is a continuation of the work of Claude Shannon, who showed that any multigraph can have its edges colored with at most (3/2)Δ colors (a tight bound, as a triangle with Δ/2 edges per side requires this many colors). Although Vizing's theorem is now standard material in many graph theory textbooks, Vizing had trouble publishing the result initially, and his paper on it appears in an obscure journal, Diskret. Analiz. Vizing also made other contributions to graph theory and graph coloring, including the introduction of list coloring,[V76] the formulation of the total coloring conjecture (still unsolved) stating that the edges and vertices of any graph can together be colored with at most Δ + 2 colors,[V68] Vizing's conjecture (also unsolved) concerning the domination number of cartesian products of graphs,[V68] and the 1974 definition of the modular product of graphs as a way of reducing subgraph isomorphism problems to finding maximum cliques in graphs.[V74] He also proved a stronger version of Brooks' theorem that applies to list coloring. From 1976, Vizing stopped working on graph theory and studied problems of scheduling instead, only returning to graph theory again in 1995.

Awards Great Silver Medal of the Institute of Mathematics of the Siberian Department of the Russian Academy of Sciences

Selected publications

Notes

References

External links List of recent publications of Vadim Vizing and mathnet.ru

Worked examples

Example 1 — a first encounter with Vadim G. Vizing

Start with the simplest possible case. Write down what Vadim G. Vizing 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 Vadim G. Vizing 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 Vadim G. Vizing 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 Vadim G. Vizing

In research: Vadim G. Vizing 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 Vadim G. Vizing 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: Vadim G. Vizing is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1937 births, 2017 deaths, Graph theorists, so understanding it makes those chapters shorter.
In everyday life: Look for Vadim G. Vizing 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 Vadim G. Vizing in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Vadim G. Vizing 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.
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Frequently asked questions

What is Vadim G. Vizing in simple terms?

Why does Vadim G. Vizing 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 Vadim G. Vizing?

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 Vadim G. Vizing.