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On the Maximum Number of Cliques in a Graph

โœ Scribed by David R. Wood


Publisher
Springer Japan
Year
2007
Tongue
English
Weight
192 KB
Volume
23
Category
Article
ISSN
0911-0119

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Denote the number of vertices of G by ]G[. A clique of graph G is a maximal complete subgraph. The density oJ(G) is the number of vertices in the largest clique of G. If ยขo(G)>~ยฝ ]GI, then G has at most 2 tยฐl-'cG) cliques. The extremal graphs are then examined as wen. ## Terminology We will be co

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## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__โ€‰=โ€‰__q__โ€‰โˆ’โ€‰__p__โ€‰=โ€‰1. We show that __G__ has at most ${15\over 16} 2^{r}$ cycles. We also show that if __G__ is planar, then __G__ has at most 2^__r__โ€‰โˆ’โ€‰1^โ€‰=โ€‰__o__(2^__r__โ€‰โˆ’โ€‰1^) cycles. The planar result is best possib