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| Victor V. Vizing | |
|---|---|
| Name | Victor V. Vizing |
| Birth date | 1937 |
| Birth place | Moscow Oblast |
| Death date | 2010 |
| Nationality | Soviet / Russia |
| Fields | Mathematics |
| Workplaces | Steklov Institute, Moscow State University |
| Alma mater | Moscow State University |
| Known for | Vizing's theorem, edge coloring |
Victor V. Vizing was a Soviet and Russian mathematician noted for foundational work in graph theory, especially in edge coloring and chromatic index problems. His discoveries influenced combinatorics, algorithm design, and applications across computer science, operations research, and network theory. Vizing's career spanned research at major Soviet institutions and interactions with mathematicians in Europe and North America through publications and conferences.
Vizing was born in Moscow Oblast and completed his undergraduate and graduate studies at Moscow State University under the intellectual milieu created by figures from the Steklov Institute and the broader Soviet school that included scholars affiliated with Mikhail Lavrentyev, Israel Gelfand, Andrey Kolmogorov, Pavel Alexandrov, Andrey Tikhonov, Sergei Sobolev, Lazar Lyusternik, and contemporaries connected to Nikolai Luzin. His formative years coincided with developments at institutions such as Keldysh Institute of Applied Mathematics, Lebedev Physical Institute, and interactions with researchers from Leningrad State University and institutes linked to Academy of Sciences of the USSR. Vizing received mentorship influenced by traditions from mathematicians like Evgeny Lifshitz and exchanges that touched researchers in Prague, Budapest, Warsaw, and later contacts with visiting scholars from United States universities including Princeton University and University of California, Berkeley.
Vizing held research positions at the Steklov Institute of Mathematics and lectured at Moscow State University, collaborating with staff from centers such as Institute of Control Sciences, Institute of Applied Mathematics, and research groups associated with Soviet Academy of Sciences programs. He participated in conferences alongside mathematicians from École Normale Supérieure, University of Cambridge, University of Oxford, Massachusetts Institute of Technology, Harvard University, Stanford University, Yale University, Columbia University, University of Chicago, and institutes in Israel, Germany, France, and Japan. Vizing's academic trajectory intersected with contemporary theorists including Paul Erdős, László Lovász, Claude Berge, Kazimierz Kuratowski, William Tutte, W. T. Tutte, Ronald Graham, Richard Karp, Michael O. Rabin, Donald Knuth, and later generations such as Noga Alon and Miklós Simonovits.
Vizing formulated results that reshaped graph theory and combinatorics, particularly in edge coloring, bounds on the chromatic index, structural analysis of multigraphs, and problems related to graph factorization and matchings. He advanced techniques later used by researchers like Paul Seymour, Neil Robertson, Robin Thomas, fan method adopters, and those working on the four color theorem context such as Kenneth Appel and Wolfgang Haken. Vizing’s ideas influenced algorithmic work by scientists associated with ACM, SIAM, and practitioners in telecommunication and scheduling theory fields, linking to applied research at Bell Labs, IBM Research, and university groups at Cornell University and ETH Zurich.
Vizing is best known for Vizing's theorem which states that the chromatic index of a simple graph is either its maximum degree or that degree plus one, a classification that defined what became known as Vizing classes (Class 1 and Class 2). He also proposed the Vizing conjecture concerning the domination number of Cartesian product graphs, which stimulated work by researchers including Gary Chartrand, Paolo R. J. Östergård, Tibor Gallai, Sándor Szegedy, János Pach, Endre Szemerédi, and those exploring domination theory like M. Behzad and F. Harary. Extensions and related problems gave rise to conjectures and results connecting to the Total coloring conjecture posited by Behzad and Vizing jointly, and to structural theorems used by László Lovász and Paul Erdős in extremal graph theory. Vizing’s questions motivated work by combinatorialists such as Béla Bollobás, Erdős–Rényi model analysts, and algorithm designers like Michael Garey and David S. Johnson.
Throughout his career Vizing received recognition from Soviet and international bodies, being cited in proceedings of organizations such as International Mathematical Union, European Mathematical Society, American Mathematical Society, and publications from Springer-Verlag and Elsevier. His work is commemorated in special journal issues alongside contributions by László Lovász, Paul Erdős, Ronald Graham, Endre Szemerédi, and Fan Chung. Conferences in Graph Theory and Combinatorics held in cities like Moscow, Prague, Budapest, Paris, Berlin, New York, Boston, Tokyo, and Beijing have featured sessions honoring his legacy; proceedings were published by organizations including SIAM and Cambridge University Press.
Key papers by Vizing were published in leading Soviet journals and translated outlets, appearing alongside work by Kazimierz Kuratowski, André Lichnerowicz, Alexander Grothendieck, John von Neumann-era references, and in collections edited by figures such as Israel Gelfand and Andrey Kolmogorov. His concise proofs and conjectures continue to appear in textbooks and monographs by J. A. Bondy, U. S. R. Murty, Douglas West, Harold N. Gabow, Sanjeev Khanna, Miklós Bóna, Richard Stanley, and survey articles by Noga Alon and Joel H. Spencer. Vizing’s influence persists in contemporary research programs at institutions like Princeton University, University of Cambridge, ETH Zurich, École Polytechnique, University of Tokyo, and in algorithmic studies connected to Google and Microsoft Research. His theorems remain central in curricula and ongoing investigations by specialists including C. Thomassen, Maria Chudnovsky, Sophie Morel, Jacob Fox, and Lisa Sauermann.
Category:Mathematicians Category:Graph theorists Category:Soviet mathematicians Category:Russian mathematicians