Anton Kotzig
Encyclopedia
Anton Kotzig was a Slovak–Canadian mathematician
, expert in statistics
, combinatorics
and graph theory
. The Ringel-Kotzig conjecture on graceful labeling of trees
is named after him and Gerhard Ringel
.
, a village in Western Slovakia
, in 1919. He studied at the secondary grammar school in Nové Mesto nad Váhom
, and began his undergraduate studies at Charles University in Prague
. After the closure of Czech
universities in 1939, he moved to Bratislava
, where after the war he earned a doctoral degree (RNDr.) in mathematical statistics
from Comenius University in Bratislava
. He remained in Bratislava working at the Central Bureau of Social Insurance for Slovakia, as the head of department of mathematical statistics. Later he published a book on economy planning. Since 1951 to 1959 he was lecturing at Vysoká škola Ekonomická (today University of Economics in Bratislava
), where he served as rector
from 1952 to 1958. Thus he spent 20 years in close contact with applications of mathematics.
In 1959 he left the University of Economics to become the head of the newly created Mathematical Institute of the Slovak Academy of Sciences
, where he remained until 1964. From 1965 to 1969 he was head of department of Applied Mathematics on Faculty of natural sciences of Comenius University, where he was also dean for one year. He also earned a habilitation
degree (DrSc.) from Charles University in 1961 for thesis from graph theory
(relation and regular relation of finite graphs). Already in 1969 the list of his publications included more than 60 articles and 4 books. More of his results from 50. and 60. became classic, e.g. results concerning graph relations, 1-factors and cubic graph
s. As they were published in Slovak,
many of them remained unknown and some of the results was independently rediscovered much later by other mathematicians.
One of his arguments is generally known as Kotzigs theorem. Prof. Kotzig established today well known slovak school of graph theory. One of his first students was RNDR. Juraj Bosák, DrSc. For his work, he was awarded the Czechoslovak State Prize in 1969.
In 1969, Kotzig came to Canada, and spent a year at the University of Calgary
. He then joined the University of Montreal
in 1970, where he remained until his death. Because of the political situation, he could not travel back to Czechoslovakia
, and remained in his adopted country without his books and notes. Although he was separated from his slovak students, he started again. The result was more than 75 articles, supervision of many magister and doctor (PhD.) theses, but also very successful university lecture courses. His results concern a wide range of problems, from convex polyhedrons, Hamiltonian paths, through Latin squares and decompositions of complete graphs and also combinatorics games. In honor of his 60. birthday the publication „Theory and Practice of Combinatorics“ was published, in which experts from all around the world contributed. Prof. Kotzig published many inspiring open problems. One of them is the still unresolved Ringel-Kotzig hypothesis. He died on April 20. 1991 in Montreal
, leaving his wife Edita, and a son Ľuboš. In 1999 a commemorative plaque was erected on his birth house in Kočovce on the anniversary of his 80 years.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, expert in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
and graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
. The Ringel-Kotzig conjecture on graceful labeling of trees
Tree (graph theory)
In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...
is named after him and Gerhard Ringel
Gerhard Ringel
Gerhard Ringel was a German mathematician who earned his Ph.D. from the University of Bonn in 1951...
.
Biography
Kotzig was born in KočovceKocovce
Kočovce is a village and municipality in Nové Mesto nad Váhom District in the Trenčín Region of western Slovakia.-Geography:The municipality lies at an altitude of 183 metres and covers an area of 15.319 km². It has a population of about 1400 people....
, a village in Western Slovakia
Slovakia
The Slovak Republic is a landlocked state in Central Europe. It has a population of over five million and an area of about . Slovakia is bordered by the Czech Republic and Austria to the west, Poland to the north, Ukraine to the east and Hungary to the south...
, in 1919. He studied at the secondary grammar school in Nové Mesto nad Váhom
Nové Mesto nad Váhom
Nové Mesto nad Váhom is a town in the Trenčín Region of Slovakia.- Geography :District town located at the northern edge of the Danubian Hills at the foothills of the northern end of the White Carpathians, on the Váh river. Other mountains nearby are the White Carpathians and the Považský Inovec...
, and began his undergraduate studies at Charles University in Prague
Prague
Prague is the capital and largest city of the Czech Republic. Situated in the north-west of the country on the Vltava river, the city is home to about 1.3 million people, while its metropolitan area is estimated to have a population of over 2.3 million...
. After the closure of Czech
Czech Republic
The Czech Republic is a landlocked country in Central Europe. The country is bordered by Poland to the northeast, Slovakia to the east, Austria to the south, and Germany to the west and northwest....
universities in 1939, he moved to Bratislava
Bratislava
Bratislava is the capital of Slovakia and, with a population of about 431,000, also the country's largest city. Bratislava is in southwestern Slovakia on both banks of the Danube River. Bordering Austria and Hungary, it is the only national capital that borders two independent countries.Bratislava...
, where after the war he earned a doctoral degree (RNDr.) in mathematical statistics
Mathematical statistics
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis...
from Comenius University in Bratislava
Comenius University in Bratislava
Comenius University in Bratislava is the largest university in Slovakia, with most of its faculties located in Bratislava. It was founded in 1919, shortly after the creation of Czechoslovakia. It is named after Jan Amos Comenius, a 17th century Czech teacher and philosopher.In 2006, Comenius...
. He remained in Bratislava working at the Central Bureau of Social Insurance for Slovakia, as the head of department of mathematical statistics. Later he published a book on economy planning. Since 1951 to 1959 he was lecturing at Vysoká škola Ekonomická (today University of Economics in Bratislava
University of Economics in Bratislava
University of Economics in Bratislava is the oldest university of economics in Slovakia.-History:The university was established in 1940 as a private university under the name...
), where he served as rector
Rector
The word rector has a number of different meanings; it is widely used to refer to an academic, religious or political administrator...
from 1952 to 1958. Thus he spent 20 years in close contact with applications of mathematics.
In 1959 he left the University of Economics to become the head of the newly created Mathematical Institute of the Slovak Academy of Sciences
Slovak Academy of Sciences
The Slovak Academy of Sciences SAV is the main scientific and research institution in Slovakia fostering basic and strategic basic research...
, where he remained until 1964. From 1965 to 1969 he was head of department of Applied Mathematics on Faculty of natural sciences of Comenius University, where he was also dean for one year. He also earned a habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
degree (DrSc.) from Charles University in 1961 for thesis from graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
(relation and regular relation of finite graphs). Already in 1969 the list of his publications included more than 60 articles and 4 books. More of his results from 50. and 60. became classic, e.g. results concerning graph relations, 1-factors and cubic graph
Cubic graph
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs....
s. As they were published in Slovak,
many of them remained unknown and some of the results was independently rediscovered much later by other mathematicians.
One of his arguments is generally known as Kotzigs theorem. Prof. Kotzig established today well known slovak school of graph theory. One of his first students was RNDR. Juraj Bosák, DrSc. For his work, he was awarded the Czechoslovak State Prize in 1969.
In 1969, Kotzig came to Canada, and spent a year at the University of Calgary
University of Calgary
The University of Calgary is a public research university located in Calgary, Alberta, Canada. Founded in 1966 the U of C is composed of 14 faculties and more than 85 research institutes and centres.More than 25,000 undergraduate and 5,500 graduate students are currently...
. He then joined the University of Montreal
Université de Montréal
The Université de Montréal is a public francophone research university in Montreal, Quebec, Canada. It comprises thirteen faculties, more than sixty departments and two affiliated schools: the École Polytechnique and HEC Montréal...
in 1970, where he remained until his death. Because of the political situation, he could not travel back to Czechoslovakia
Czechoslovakia
Czechoslovakia or Czecho-Slovakia was a sovereign state in Central Europe which existed from October 1918, when it declared its independence from the Austro-Hungarian Empire, until 1992...
, and remained in his adopted country without his books and notes. Although he was separated from his slovak students, he started again. The result was more than 75 articles, supervision of many magister and doctor (PhD.) theses, but also very successful university lecture courses. His results concern a wide range of problems, from convex polyhedrons, Hamiltonian paths, through Latin squares and decompositions of complete graphs and also combinatorics games. In honor of his 60. birthday the publication „Theory and Practice of Combinatorics“ was published, in which experts from all around the world contributed. Prof. Kotzig published many inspiring open problems. One of them is the still unresolved Ringel-Kotzig hypothesis. He died on April 20. 1991 in Montreal
Montreal
Montreal is a city in Canada. It is the largest city in the province of Quebec, the second-largest city in Canada and the seventh largest in North America...
, leaving his wife Edita, and a son Ľuboš. In 1999 a commemorative plaque was erected on his birth house in Kočovce on the anniversary of his 80 years.
External links
- Anton Kotzig, 1919–1991, Mathematica Slovaca 42:3 (1992) 381-383.
- Prof. Anton Kotzig's biography (in SlovakSlovak languageSlovak , is an Indo-European language that belongs to the West Slavic languages .Slovak is the official language of Slovakia, where it is spoken by 5 million people...
).