Hypergraph Turán Problems

@inproceedings{Keevash2011HypergraphTP,
  title={Hypergraph Tur{\'a}n Problems},
  author={Peter Keevash},
  year={2011}
}
One of the earliest results in Combinatorics is Mantel’s theorem from 1907 that the largest triangle-free graph on a given vertex set is complete bipartite. However, a seemingly similar question posed by Turán in 1941 is still open: what is the largest 3-uniform hypergraph on a given vertex set with no tetrahedron? This question can be considered a test case for the general hypergraph Turán problem, where given an r-uniform hypergraph F , we want to determine the maximum number of edges in an r… CONTINUE READING

Figures from this paper.

Citations

Publications citing this paper.
SHOWING 1-10 OF 135 CITATIONS

New Short Proofs to Some Stability Theorems

VIEW 5 EXCERPTS
CITES METHODS
HIGHLY INFLUENCED

Continuous optimisation in extremal combinatorics

VIEW 8 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Edges not in any monochromatic copy of a fixed graph

  • J. Comb. Theory, Ser. B
  • 2017
VIEW 5 EXCERPTS
CITES RESULTS
HIGHLY INFLUENCED

Lagrangians of hypergraphs: The Frankl-Füredi conjecture holds almost everywhere

  • J. London Math. Society
  • 2017
VIEW 5 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

A rainbow Erdős-Rothschild problem

  • Electronic Notes in Discrete Mathematics
  • 2015
VIEW 7 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Stability and Turán Numbers of a Class of Hypergraphs via Lagrangians

  • Combinatorics, Probability & Computing
  • 2015
VIEW 11 EXCERPTS
CITES RESULTS & BACKGROUND
HIGHLY INFLUENCED

An extension of the Motzkin-Straus theorem to non-uniform hypergraphs and its applications

  • Discrete Applied Mathematics
  • 2013
VIEW 6 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Thresholds in probabilistic and extremal combinatorics

VIEW 8 EXCERPTS
CITES RESULTS, BACKGROUND & METHODS
HIGHLY INFLUENCED

FILTER CITATIONS BY YEAR

2009
2019

CITATION STATISTICS

  • 20 Highly Influenced Citations

  • Averaged 23 Citations per year from 2017 through 2019