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arXiv · 1002.1270

Trees with Given Stability Number and Minimum Number of Stable Sets

Véronique Bruyère·Gwenaël Joret·Hadrien Mélot
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Abstract

We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $α$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-α$ stars, each of size $\lceil \frac{n-1}{n-α} \rceil$ or $\lfloor \frac{n-1}{n-α}\rfloor$, 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.

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Véronique Bruyère, Gwenaël Joret, Hadrien Mélot. 2011-03-04. Trees with Given Stability Number and Minimum Number of Stable Sets. https://doi.org/10.1007/s00373-011-1041-2

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