Size of a phylogenetic network. (English) Zbl 1358.05266
Summary: We consider the problem of when the total number \(n\) of vertices in a phylogenetic network \(\mathcal{N}\) is bounded by the number \(\ell\) of leaves in \(\mathcal{N}\). The main result of the paper says that, provided \(\mathcal{N}\) avoids three certain substructures, then \(n\) is at most quadratic in \(\ell\). Furthermore, if any of these substructures is present in \(\mathcal{N}\), then \(\ell\) does not necessarily bound \(n\).
MSC:
| 05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
| 90B10 | Deterministic network models in operations research |
References:
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