%0 Journal Article
%T Trees with Given Stability Number and Minimum Number of Stable Sets
%A V¨¦ronique Bruy¨¨re
%A Gwena£¿l Joret
%A Hadrien M¨¦lot
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s00373-011-1041-2
%X We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of size $\lceil \frac{n-1}{n-\alpha} \rceil$ or $\lfloor \frac{n-1}{n-\alpha}\rfloor$, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.
%U http://arxiv.org/abs/1002.1270v2