Brouwer, A. E.; Mills, C. F.; Mills, W. H.; Verbeek, A. Counting families of mutually intersecting sets. (English) Zbl 1267.05144 Electron. J. Comb. 20, No. 2, Research Paper P8, 8 p. (2013). Summary: We show that the number of maximal intersecting families on a 9-set equals 423295099074735261880, that the number of independent sets of the Kneser graph \(K(9,4)\) equals \[ 366996244568643864340, \] and that the number of intersecting families on an 8-set and on a 9-set is \[ 14704022144627161780744368338695925293142507520 \]and\[ \begin{split} 125532424879405039143639827181122982679752727208\\08010757809032705650591023015520462677475328\end{split} \] (roughly \(1.255\cdot 10^{91}\)), respectively. Cited in 3 Documents MSC: 05C30 Enumeration in graph theory 05C75 Structural characterization of families of graphs Keywords:maximal linked systems; Kneser graph; counting independent sets PDF BibTeX XML Cite \textit{A. E. Brouwer} et al., Electron. J. Comb. 20, No. 2, Research Paper P8, 8 p. (2013; Zbl 1267.05144) Full Text: Link