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
โฆ LIBER โฆ
On the Maximum Number of Cliques in a Graph
โ 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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## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__โ=โ__q__โโโ__p__โ=โ1. 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__โโโ1^โ=โ__o__(2^__r__โโโ1^) cycles. The planar result is best possib