On the Ramsey multiplicity of complete graphs

@article{Conlon2012OnTR,
  title={On the Ramsey multiplicity of complete graphs},
  author={David Conlon},
  journal={Combinatorica},
  year={2012},
  volume={32},
  pages={171-186}
}
We show that, for n large, there must exist at least nt C(1+o(1))t monochromatic Kts in any two-colouring of the edges of Kn, where C ≈ 2.18 is an explicitly defined constant. The old lower bound, due to Erdős [E62], and based upon the standard bounds for Ramsey’s theorem, is nt 4(1+o(1))t . 

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Showing 1-10 of 13 references

On Erdős’s conjecture on multiplicites of complete subgraphs, Combinatorica

F. Franek, V. Rödl
2002

Rödl : 2colourings of complete graphs with small number of monochromatic K 4 subgraphs

V. F. Franek
Discrete Mathematics • 1993

Thomason : A disproof of a conjecture of Erdős in Ramsey theory

A.
J . London Math . Soc . • 1989

Szekely : On the number of homogeneous subgraphs of a graph

A. L.
1984

Rödl : On Erdős ’ s conjecture on multiplicites of complete subgraphs Giraud : Sur la problème de Goodman pour les quadrangles et la majoration des nombres de Ramsey

V. F. Franek
1979

On the number of complete subgraphs contained in certain graphs

P. Erdős
Publ. Math. Inst. Hung. Acad. Sci., VII, Ser. A • 1962

On sets of acquaintances and strangers at any party

A. W. Goodman
Amer. Math. Monthly, • 1959

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