Extremal Hypergraphs and Combinatorial Geometry
نویسنده
چکیده
Here we overview some of the methods and results of extremal graph and hypergraph theory. A few geometric applications are also given.
منابع مشابه
Ryan Martin
The focus of my research is extremal graph theory and random combinatorial structures. I have also worked in a variety of other areas, including intersecting hypergraphs, the theory of positional games and Ramsey theory. Combinatorics, and particularly graph theory, has a wide variety of applications. My own research in the edit distance of graphs has applications in biology and computer scienc...
متن کاملEdit Distance in Graphs
The focus of my research is extremal graph theory and random combinatorial structures. I have also worked in a variety of other areas, including intersecting hypergraphs, the theory of positional games and Ramsey theory. I use a number of tools in my research, notably probabilistic methods and, most prominently, Szemerédi’s regularity lemma. I have used these and other techniques to address que...
متن کاملQuasi-Random Hypergraphs and Extremal Problems for Hypergraphs
The regularity lemma was originally developed by Szemerédi in the seventies as a tool to resolve a long standing conjecture of Erdős and Turán, that any subset of the integers of positive upper density contains arbitrary long arithmetic progressions. Soon this lemma was recognized as an important tool in extremal graph theory and it also has had applications to additive number theory, discrete ...
متن کاملDensity Theorems and Extremal Hypergraph Problems
We present alternative proofs of density versions of some combinatorial partition theorems originally obtained by H. Furstenberg and Y. Katznelson. These proofs are based on an extremal hypergraph result which was recently independently obtained by W. T. Gowers and B. Nagle, V. Rödl, M. Schacht, J. Skokan by extending Szemerédi’s regularity lemma to hypergraphs.
متن کاملTechnical Report TR - 2004 - 021 Density Theorems and Extremal Hypergraph Problems
We present alternative proofs of density versions of some combinatorial partition theorems originally obtained by H. Furstenberg and Y. Katznelson. These proofs are based on an extremal hypergraph result which was recently independently obtained by W. T. Gowers and B. Nagle, V. Rödl, M. Schacht, J. Skokan by extending Szemerédi’s Regularity Lemma to hypergraphs.
متن کامل