Geodesic
A Cantor-Bendixson rank for siblings of trees
Davoud Abdi1
1University of Calgary
The electronic journal of combinatorics, Tome 30 (2023) no. 2
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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 $T^\infty$ with some leafy trees attached to $T^\infty$. With this representation at our disposal, we count the siblings of a tree and obtain partial results towards a conjecture of Bonato and Tardif.
DOI : 10.37236/11537
Classification : 05C05, 05C10
Mots-clés : rayless tree, self-embedding, Bonato-Tardif conjecture

Davoud Abdi  1

1 University of Calgary 
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Davoud Abdi. A Cantor-Bendixson rank for siblings of trees. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11537

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