A Cantor-Bendixson Rank for Siblings of Trees
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 $T^\infty$....
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| Veröffentlicht in: | The Electronic journal of combinatorics 2023-05, Vol.30 (2) |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/11537 |