Galled Tree-Child Networks
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910354133483520 |
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| author | Chang, Yu-Sheng Fuchs, Michael Yu, Guan-Ru |
| author_facet | Chang, Yu-Sheng Fuchs, Michael Yu, Guan-Ru |
| contents | We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asymptotic) counting results and stochastic results have been proved with very different methods. We show that a counting result for the class of galled tree-child networks follows with similar tools as used for galled networks, however, the result has a similar pattern as the one for tree-child networks. In addition, we also consider the (suitably scaled) numbers of reticulation nodes of random galled tree-child networks and show that they are asymptotically normal distributed. This is in contrast to the limit laws of the corresponding quantities for galled networks and tree-child networks which have been both shown to be discrete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galled Tree-Child Networks Chang, Yu-Sheng Fuchs, Michael Yu, Guan-Ru Combinatorics 05C20, 60C05, 60F05, 92D15 We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asymptotic) counting results and stochastic results have been proved with very different methods. We show that a counting result for the class of galled tree-child networks follows with similar tools as used for galled networks, however, the result has a similar pattern as the one for tree-child networks. In addition, we also consider the (suitably scaled) numbers of reticulation nodes of random galled tree-child networks and show that they are asymptotically normal distributed. This is in contrast to the limit laws of the corresponding quantities for galled networks and tree-child networks which have been both shown to be discrete. |
| title | Galled Tree-Child Networks |
| topic | Combinatorics 05C20, 60C05, 60F05, 92D15 |
| url | https://arxiv.org/abs/2403.02923 |