A split system on a multiset $\mathcal M$ is a multiset of bipartitions of $\mathcal M$. Such a split system $\mathfrak S$ 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 $\mathcal M$, the removal of each edge in the tree yields a bipartition in $\mathfrak S$ by taking the labels of the two resulting components, and every bipartition in $\mathfrak S$ 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.
@article{10_37236_10974,
author = {Vincent Moulton and Guillaume Scholz},
title = {Compatible split systems on a multiset},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/10974},
zbl = {7975080},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10974/}
}
TY - JOUR
AU - Vincent Moulton
AU - Guillaume Scholz
TI - Compatible split systems on a multiset
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10974/
DO - 10.37236/10974
ID - 10_37236_10974
ER -
%0 Journal Article
%A Vincent Moulton
%A Guillaume Scholz
%T Compatible split systems on a multiset
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10974/
%R 10.37236/10974
%F 10_37236_10974
Vincent Moulton; Guillaume Scholz. Compatible split systems on a multiset. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/10974
