Geodesic
Almost all trees have an even number of independent sets
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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This paper is devoted to the proof of the surprising fact that almost all trees have an even number of independent vertex subsets (in the sense that the proportion of those trees with an odd number of independent sets tends to $0$ as the number of vertices approaches $\infty$) and to its generalisation to other moduli: for fixed $m$, the probability that a randomly chosen tree on $n$ vertices has a number of independent subsets that is divisible by $m$ tends to $1$ as $n \to \infty$.
DOI : 10.37236/182
Classification : 05C30, 05A16, 05C05, 05C69 
@article{10_37236_182,
     author = {Stephan G. Wagner},
     title = {Almost all trees have an even number of independent sets},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/182},
     zbl = {1230.05165},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/182/}
}
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Stephan G. Wagner. Almost all trees have an even number of independent sets. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/182

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