mathematics

Víctor Neumann-Lara

Víctor Neumann-Lara 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 Víctor Neumann-Lara rather than just read about it. In short: Víctor Neumann-Lara (1933–2004) was a Mexican mathematician and a pioneer in the field of graph theory in Mexico. His work also covers general topology, game theory and combinatorics.

Key takeaways

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

Reference excerpt

Víctor Neumann-Lara (1933–2004) was a Mexican mathematician and a pioneer in the field of graph theory in Mexico. His work also covers general topology, game theory and combinatorics.

Biography Born in the city of Huejutla, Hidalgo, Mexico, he soon moved to Mexico City, where he received his bachelor's degree in mathematics from the School of Sciences, UNAM. His life was greatly devoted to teaching, giving over 100 courses in Mexico and around the world, and introducing new teaching methods. He carried color chalks with him all the time, and was prompt to give graphic explanations.

Work Full Professor at the Institute of Mathematics, UNAM, he directed over 15 theses and taught both in the Institute and in the Faculty of Sciences. Below is a selection of his multiple publications, which earned him over 120 citations from renowned mathematicians in the area of graph theory. In 1982 he introduced the notion of a dichromatic number of a digraph, which would eventually be used in kernel theory and tournament theory.

Selected publications Francisco Larrión, Víctor Neumann-Lara, Miguel A. Pizaña, Thomas Dale Porter "A hierarchy of self-clique graphs" Discrete Mathematics 282(1–3): 193–208 (2004) M. E. Frías-Armenta, Víctor Neumann-Lara, Miguel A. Pizaña "Dismantlings and iterated clique graphs" Discrete Mathematics 282(1–3): 263–265 (2004) Xueliang Li, Víctor Neumann-Lara, Eduardo Rivera-Campo "On a tree graph defined by a set of cycles" Discrete Mathematics 271(1–3): 303–310 (2003) Juan José Montellano-Ballesteros, Víctor Neumann-Lara "An Anti-Ramsey Theorem" Combinatorica 22(3): 445–449 (2002) Francisco Larrión, Víctor Neumann-Lara "On clique divergent graphs with linear growth" Discrete Mathematics 245(1–3): 139–153 (2002) Francisco Larrión, Víctor Neumann-Lara, Miguel A. Pizaña "Whitney triangulations, local girth and iterated clique graphs" Discrete Mathematics 258(1–3): 123–135 (2002) Francisco Larrión, Víctor Neumann-Lara, Miguel A. Pizaña "On the homotopy type of the clique graph" J. Braz. Comp. Soc. 7(3): 69–73 (2001) Francisco Larrión, Víctor Neumann-Lara "Locally C6 graphs are clique divergent" Discrete Mathematics 215: 159–170 (2000) Manuel Abellanas, G. Hernandez, Rolf Klein, Víctor Neumann-Lara, Jorge Urrutia "A Combinatorial Property of Convex Sets" Discrete & Computational Geometry 17(3): 307–318 (1997) Manuel Abellanas, G. Hernandez, Rolf Klein, Víctor Neumann-Lara, Jorge Urrutia "Voronoi Diagrams and Containment of Families of Convex Sets on the Plane" Symposium on Computational Geometry 71–78 (1995) Jorge L. Arocha, Javier Bracho, Víctor Neumann-Lara "Tight and Untight Triangulations of Surfaces by Complete Graphs" J. Comb. Theory, Ser. B 63(2): 185–199 (1995) Víctor Neumann-Lara, Eduardo Rivera-Campo "Spanning trees with bounded degrees" Combinatorica 11(1): 55–61 (1991) Roland Häggkvist, Pavol Hell, Donald J. Miller, Víctor Neumann-Lara "On multiplicative graphs and the product conjecture" Combinatorica 8(1): 63–74 (1988) Víctor Neumann-Lara, H. Galeana-Sánchez "On kernel-perfect critical digraphs" Discrete Math. 59: 257–265 (1986) Víctor Neumann-Lara, N. Santorro, Jorge Urrutia "Uniquely colourable m-dichromatic oriented graphs" Discrete Math. 62: 65–70 (1986) Víctor Neumann-Lara, Luis Montejano "A variation of Menger's theorem for long paths" J. Combin. Theory Ser. B 36: 213–217 (1984) Víctor Neumann-Lara, Jorge Urrutia "Vertex critical r-dichromatic tournaments" Discrete Math. 49: 83–87 (1984) Víctor Neumann-Lara, H. Galeana-Sanchez "On kernels and semikernels of digraphs" Discrete Math. 48: 67–76 (1984) Víctor Neumann-Lara "The dichromatic number of a digraph" J. Combin. Theory Ser. B 33: 265–270 (1982) Víctor Neumann-Lara "k-Hamiltonian graphs with given girth" Colloq. Math. Soc. János Bolyai 10: 1133–1142 (1975)

References

A short biography in Spanish

External links Graph Theory white pages Víctor Neumann-Lara at the Mathematics Genealogy Project Victor Neumann-Lara at DBLP Bibliography Server

Mexican Jews

Illustrations

Worked examples

Example 1 — a first encounter with Víctor Neumann-Lara

Start with the simplest possible case. Write down what Víctor Neumann-Lara 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 Víctor Neumann-Lara 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 Víctor Neumann-Lara 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 Víctor Neumann-Lara

In research: Víctor Neumann-Lara 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 Víctor Neumann-Lara 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: Víctor Neumann-Lara is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1933 births, 2004 deaths, 20th-century Mexican mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Víctor Neumann-Lara 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 Víctor Neumann-Lara in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Víctor Neumann-Lara 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 Víctor Neumann-Lara out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Víctor Neumann-Lara in simple terms?

Víctor Neumann-Lara (1933–2004) was a Mexican mathematician and a pioneer in the field of graph theory in Mexico. His work also covers general topology, game theory and combinatorics.

Why does Víctor Neumann-Lara 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 Víctor Neumann-Lara?

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 Víctor Neumann-Lara.