How many graphs are unions of k-cliques?
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BΓ©la BollobΓ‘s; Graham R. Brightwell
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Article
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2006
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John Wiley and Sons
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English
β 171 KB
## Abstract We study the number $ F [n;k] $ of __n__βvertex graphs that can be written as the edgeβunion of __k__βvertex cliques. We obtain reasonably tight estimates for $ F [n;k] $ in the cases (i) kβ=βnβββo(n) and (ii) kβ=βo(n) but $ k/log\, n \to\infty $. We also show that $ F [n;k] $ exhibits