×

zbMATH — the first resource for mathematics

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.

MSC:
05C35 Extremal problems in graph theory
05C30 Enumeration in graph theory
Keywords:
upper bound; cliques
PDF BibTeX XML Cite
Full Text: DOI
References:
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.