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arXiv · 2403.02923

Galled Tree-Child Networks

Yu-Sheng Chang·Michael Fuchs·Guan-Ru Yu
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Abstract

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.

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Yu-Sheng Chang, Michael Fuchs, Guan-Ru Yu. 2024-03-05. Galled Tree-Child Networks. https://arxiv.org/abs/2403.02923

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