167 research outputs found
An efficient container lemma
We prove a new, efficient version of the hypergraph container theorems that
is suited for hypergraphs with large uniformities. The main novelty is a
refined approach to constructing containers that employs simple ideas from
high-dimensional convex geometry. The existence of smaller families of
containers for independent sets in such hypergraphs, which is guaranteed by the
new theorem, allows us to improve upon the best currently known bounds for
several problems in extremal graph theory, discrete geometry, and Ramsey
theory.Comment: 56 pages, revised versio
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
Recommended from our members
Combinatorics
Combinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization, Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions. This is a report on the meeting, containing abstracts of the presentations and a summary of the problem session
- …