Clique numbers of graphs

Paul Erdös, Marcel Erné

Research output: Contribution to journalArticle

3 Citations (Scopus)


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(2n · n-2/5) and show that all natural numbers between n + 1 and 2n-6n5/6 belong to G(n). Thus we obtain lim n→∞ |G(n)| 2n=0, while lim n→∞ |G(n)| an= ∞ for all 0 < a < 2.

Original languageEnglish
Pages (from-to)235-242
Number of pages8
JournalDiscrete Mathematics
Issue number3
Publication statusPublished - May 1986

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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