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- W2738402261 abstract "A tree-based network $mathcal N$ on $X$ is universal if every rooted binary phylogenetic $X$-tree is a base tree for $mathcal N$. Hayamizu and, independently, Zhang constructively showed that, for all positive integers $n$, there exists an universal tree-based network on $n$ leaves. For all $n$, Hayamizu's construction contains $Theta(n!)$ reticulations, while Zhang's construction contains $Theta(n^2)$ reticulations. A simple counting argument shows that an universal tree-based network has $Omega(nlog n)$ reticulations. With this in mind, Hayamizu as well as Steel posed the problem of determining whether or not such networks exists with $O(nlog n)$ reticulations. In this paper, we show that, for all $n$, there exists an universal tree-based network on $n$ leaves with $O(nlog n)$ reticulations." @default.
- W2738402261 created "2017-07-31" @default.
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- W2738402261 date "2017-07-26" @default.
- W2738402261 modified "2023-09-27" @default.
- W2738402261 title "A universal tree-based network with the minimum number of reticulations" @default.
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