A Cantor-Bendixson Rank for Siblings of Trees
Abstract
Similar to topological spaces, we introduce the Cantor-Bendixson rank of a tree T by repeatedly removing the leaves and the isolated vertices of T using transfinite recursion. Then, we give a representation of a tree T as a leafless tree T∞ with some leafy trees attached to T∞. With this representation at our disposal, we count the siblings of a tree and obtain partial results towards a conjecture of Bonato and Tardif.
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