A sharp lower bound for the number of phylogenetic trees displayed by a tree-child network
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918127096299520 |
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| author | Semple, Charles Wicke, Kristina |
| author_facet | Semple, Charles Wicke, Kristina |
| contents | A normal (phylogenetic) network with $k$ reticulations displays $2^k$ phylogenetic trees. In this paper, we establish an analogous result for tree-child (phylogenetic) networks with no underlying $3$-cycles. In particular, we show that a tree-child network with $k\ge 2$ reticulations and no underlying $3$-cycles displays at least $2^{k/2}$ phylogenetic trees if $k$ is even and at least $\frac{3}{2\sqrt{2}}2^{k/2}$ if $k$ is odd. Moreover, we show that these bounds are sharp and characterise the tree-child networks that attain these bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A sharp lower bound for the number of phylogenetic trees displayed by a tree-child network Semple, Charles Wicke, Kristina Combinatorics Populations and Evolution A normal (phylogenetic) network with $k$ reticulations displays $2^k$ phylogenetic trees. In this paper, we establish an analogous result for tree-child (phylogenetic) networks with no underlying $3$-cycles. In particular, we show that a tree-child network with $k\ge 2$ reticulations and no underlying $3$-cycles displays at least $2^{k/2}$ phylogenetic trees if $k$ is even and at least $\frac{3}{2\sqrt{2}}2^{k/2}$ if $k$ is odd. Moreover, we show that these bounds are sharp and characterise the tree-child networks that attain these bounds. |
| title | A sharp lower bound for the number of phylogenetic trees displayed by a tree-child network |
| topic | Combinatorics Populations and Evolution |
| url | https://arxiv.org/abs/2508.13414 |