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arXiv · 2608.23275

On the maximum size of 2-weakly compatible split systems

Pei Wu·Stefan Grünewald
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Abstract

We consider a Turán-type problem arising in phylogenetics: determining the maximum size of a 2-weakly compatible split system. This compatibility condition arises in the reconstruction of phylogenetic networks from quartet weights. It was previously shown that a 2-weakly compatible split system has size at most \[ 3\binom{n}{4}+\binom{n}{2}. \] We prove that the maximum size is $O(n^{5/2})$.

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Pei Wu, Stefan Grünewald. 2026-08-24. On the maximum size of 2-weakly compatible split systems. https://arxiv.org/abs/2608.23275

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