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An upper bound on the number of cliques in a graph. (English) Zbl 0777.05070
The autors show that if the complement of a graph \(G\) of \(n\) vertices does not contain a set of \(t+1\) pairwise disjoint edges as an induced graph, then \(G\) has fewer than \((n/2t)^{2t}\) maximal complete subgraphs.

05C35 Extremal problems in graph theory
05C30 Enumeration in graph theory
upper bound; cliques
Full Text: DOI
[1] Balas, Networks 19 pp 247– (1989)
[2] Escalante, Abh. Math. Sem. Univ. Hamburg 39 pp 59– (1973)
[3] Farber, Discrete Math. 73 pp 249– (1989)
[4] Füredi, J. of Graph Theory 11 pp 463– (1987)
[5] Griggs, Discrete Math. 68 pp 211– (1988)
[6] Hedman, Discrete Math. 54 pp 161– (1985)
[7] and , The number of maximal independent sets in triangle-free graphs, SIAM J. Disc. Math, in print. · Zbl 0779.05025
[8] Moon, Israel J. Math. 3 pp 23– (1965)
[9] Sagan, SIAM J. Discrete Math. 1 pp 105– (1988)
[10] Wilf, SIAM J. Alg. Discrete Methods 7 pp 125– (1986)
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