On the number of independent sets in graphs with fixed independence number
Diskretnaya Matematika, Tome 19 (2007) no. 2, pp. 63-66
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We construct a sequence of graphs of large degree with growing number of vertices for which the number of independent sets is substantially greater than the number of all subsets of the independent set of maximal cardinality.
[1] Sapozhenko A. A., “Dokazatelstvo gipotezy Kamerona–Erdesha o chisle mnozhestv, svobodnykh ot summ”, Matem. voprosy kibern., 12 (2003), 5–14
[2] Sapozhenko A. A., “O chisle nezavisimykh mnozhestv v rasshiritelyakh”, Diskretnaya matematika, 13:1 (2001), 56–62 | MR | Zbl
[3] Kharari F., Teoriya grafov, Mir, Moskva, 1973 | MR
[4] Alon N., “Independent sets in regular graphs and sum-free subsets of finite groups”, Israel J. Math., 73:2 (1991), 247–256 | DOI | MR | Zbl