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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics