Abstract
A split system on a multiset M is a multiset of bipartitions of M. Such a split system S is compatible if it can be represented by a tree in such a way that the vertices of the tree are labelled by the elements in M, the removal of each edge in the tree yields a bipartition in S by taking the labels of the two resulting components, and every bipartition in S can be obtained from the tree in this way. Compatibility of split systems is a key concept in phylogenetics, and compatible split systems have applications to, for example, multi-labelled phylogenetic trees. In this contribution, we present a novel characterization for compatible split systems, and for split systems admitting a unique representation by a tree. In addition, we show that a conjecture on compatibility stated in 2008 holds for some large classes of split systems.
| Original language | English |
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| Journal | Electronic Journal of Combinatorics |
| Publication status | Accepted/In press - 2 Nov 2024 |