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==Graph container algorithm==
We first describe a method for showing strong upper bounds on the number of independent sets in a graph; this exposition adapted from a survey of Samotij<ref>{{cite journal |last1=Samotij |first1= Wojciech |title=Counting independent sets in graphs |journal=European Journal of Combinatorics |date=2015 |volume=48 |pages=5–18|doi= 10.1016/j.ejc.2015.02.005 |s2cid= 15850625 }}</ref> about the graph container method, originally employed by Kleitman-Winston and Sapozhenko.
 
===Notation===