Graphs and Combinatorics

, Volume 8, Issue 4, pp 299–308 | Cite as

Ramsey problem on multiplicities of complete subgraphs in nearly quasirandom graphs

  • F. Franek
  • V. Rödl
Original Papers


Letkt(G) be the number of cliques of ordert in the graphG. For a graphG withn vertices let\(c_t (G) = \frac{{k_t (G) + k_t (\bar G)}}{{\left( {\begin{array}{*{20}c} n \\ t \\ \end{array} } \right)}}\). Letct(n)=Min{ct(G)∶∇G∇=n} and let\(c_t = \mathop {\lim }\limits_{n \to \infty } c_t (n)\). An old conjecture of Erdös [2], related to Ramsey's theorem states thatct=21-(t/2). Recently it was shown to be false by A. Thomason [12]. It is known thatct(G)≈21-(t/2) wheneverG is a pseudorandom graph. Pseudorandom graphs — the graphs “which behave like random graphs” — were inroduced and studied in [1] and [13]. The aim of this paper is to show that fort=4,ct(G)≥21-(t/2) ifG is a graph arising from pseudorandom by a small perturbation.


Small Perturbation Random Graph Theorem State Complete Subgraph Ramsey Problem 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • F. Franek
    • 1
  • V. Rödl
    • 2
  1. 1.Department of Computer Science and SystemsMcMaster UniversityHamiltonCanada
  2. 2.Departments of Mathematics and Computer Science Emory UniversityAtlantaUSA

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