Compatible split systems on a multiset

Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435 and Scholz, Guillaume E. (2024) Compatible split systems on a multiset. Electronic Journal of Combinatorics, 31 (4). ISSN 1077-8926

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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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Norwich Epidemiology Centre Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre Faculty of Science > Research Groups > Computational Biology
Depositing User:	LivePure Connector
Date Deposited:	07 Nov 2024 14:30
Last Modified:	09 Jan 2025 01:02
URI:	https://ueaeprints.uea.ac.uk/id/eprint/97569
DOI:	10.37236/10974

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