Abstract:We consider the problem of the minimum number of phylogenetic trees it would take to display all splits in a given set, a problem related to k-compatibility. A set of trees that displays every single possible split is termed a universal tree set. In this note, we find the universal incompatibility U(n), the minimal size of a universal tree set for n taxa. By normalising incompatibility using U(n), one can then compare incompatibility of split systems across different numbers of taxa. We demonstrate this applic… Show more
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