### Abstract

For each natural number n, denote by G(n) the set of all numbers c such that there exists a graph with exactly c cliques (i.e., complete subgraphs) and n vertices. We prove the asymptotic estimate |G(n)| = 0(2^{n} · n^{-2/5}) and show that all natural numbers between n + 1 and 2^{n-6n5/6} belong to G(n). Thus we obtain lim n→∞ |G(n)| 2^{n}=0, while lim n→∞ |G(n)| a^{n}= ∞ for all 0 < a < 2.

Original language | English |
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Pages (from-to) | 235-242 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 59 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 1986 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Erdös, P., & Erné, M. (1986). Clique numbers of graphs.

*Discrete Mathematics*,*59*(3), 235-242. https://doi.org/10.1016/0012-365X(86)90170-6