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The concept of $k$-compatibility measures how many phylogenetic trees itwould take to display all splits in a given set. A set of trees that displayevery single possible split is termed a \textit{universal tree set}. In thisnote, we find $A(n)$, the minimal size of a universal tree set for $n$ taxa. Bynormalising the $k$-compatibility using $A(n)$, one can then compareincompatibility of split systems across different taxa sizes. We demonstratethis application by comparing two SplitsTree networks of different sizesderived from archaeal genomes.

On the comparison of incompatibility of split systems across different numbers of taxa