Lajos Pósa (mathematician)
Encyclopedia
Lajos Pósa is a Hungarian mathematician, working in combinatorics
. Paul Erdős
's favorite "child", he discovered theorems at the age of 16. Since 2002 he works at the Rényi Institute of the Hungarian Academy of Sciences
; earlier he was at the Eötvös Loránd University, at the Departments of Analysis, Computer Science. He received the Károly Simonyi Research Scholarship in 2000.
Pósa is one of the most active and most successful mathematical educators in Hungary. He taught many of the famous Hungarian mathematicians (László Babai
, Imre Z. Ruzsa
, Gábor Tardos
). Most of his students, however, do not become professional mathematicians. He organizes special 1–2 day long mathematical camps for carefully selected 12–18 year old children, one group containing 25–35 kids meeting twice a year. He does not aim to teach hard, established parts of mathematics, but rather makes the participants discover mathematical results via solving carefully chosen elementary problems in groups of 3 or 4.
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 ,...
. Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
's favorite "child", he discovered theorems at the age of 16. Since 2002 he works at the Rényi Institute of the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
; earlier he was at the Eötvös Loránd University, at the Departments of Analysis, Computer Science. He received the Károly Simonyi Research Scholarship in 2000.
Pósa is one of the most active and most successful mathematical educators in Hungary. He taught many of the famous Hungarian mathematicians (László Babai
László Babai
László Babai is a Hungarian professor of mathematics and computer science at the University of Chicago. His research focuses on computational complexity theory, algorithms, combinatorics, and finite groups, with an emphasis on the interactions between these fields...
, Imre Z. Ruzsa
Imre Z. Ruzsa
Imre Z. Ruzsa is a Hungarian mathematician specializing in number theory.Ruzsa participated in the International Mathematical Olympiad for Hungary, winning a silver medal in 1969, and two consecutive gold medals with perfect scores in 1970 and 1971. He graduated from the Eötvös Loránd University...
, Gábor Tardos
Gábor Tardos
Gábor Tardos is a Hungarian mathematician, currently a professor and Canada Research Chair at Simon Fraser University. He works mainly in combinatorics and computer science...
). Most of his students, however, do not become professional mathematicians. He organizes special 1–2 day long mathematical camps for carefully selected 12–18 year old children, one group containing 25–35 kids meeting twice a year. He does not aim to teach hard, established parts of mathematics, but rather makes the participants discover mathematical results via solving carefully chosen elementary problems in groups of 3 or 4.
Mathematical research
- He gave sufficient conditions for the existence of Hamiltonian circuitHamiltonian pathIn the mathematical field of graph theory, a Hamiltonian path is a path in an undirected graph that visits each vertex exactly once. A Hamiltonian cycle is a cycle in an undirected graph that visits each vertex exactly once and also returns to the starting vertex...
. - He proved that a random graphRandom graphIn mathematics, a random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs.-Random graph models:...
on n vertices with cn log n edges almost surely contains a Hamiltonian circuit, thus affirming a conjecture of Erdős and RényiAlfréd RényiAlfréd Rényi was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory.-Life:...
(also proved by A. D. Korshunov). The result was later improved by KomlósJános Komlós (mathematician)János Komlós is a Hungarian-American mathematician, working in probability theory and discrete mathematics. He is a professor of mathematics at Rutgers University since 1988. He graduated from the Eötvös Loránd University, then became a fellow at the Mathematical Institute of the Hungarian Academy...
and SzemerédiEndre SzemerédiEndre Szemerédi is a Hungarian mathematician, working in the field of combinatorics and theoretical computer science. He is the State of New Jersey Professor of computer science at Rutgers University since 1986...
. - With ErdősPaul ErdosPaul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
he proved the Erdős–Pósa theoremErdős–Pósa theoremIn the mathematical discipline of graph theory, the Erdős–Pósa theorem, named after Paul Erdős and Lajos Pósa, states that there is a function such for each positive integer , every graph either contains vertex-disjoint circuits or it has a feedback vertex set of vertices that intersects every...
.