Quasi-median graphs from sets of partitions

Authors:
H.-J. Bandelt;K. T. Huber;V. Moulton
Affiliations:
Fachbereich Mathematik, Universität Hamburg, D-20146 Hamburg, Germany;Physics and Mathematics Department (FMI) Mid Sweden University, S 851-70 Sundsvall, Sweden;Physics and Mathematics Department (FMI) Mid Sweden University, S 851-70 Sundsvall, Sweden
Venue:
Discrete Applied Mathematics
Year:
2002

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Abstract

In studies of molecular evolution, one is typically confronted with the task of inferring a phylogenetic tree from a set X of sequences of length n over a finite alphabet Λ. For studies that invoke parsimony, it has been found helpful to consider the quasi-median graph generated by X in the Hamming graph Λn. Although a great deal is already known about quasi-median graphs (and their algebraic counterparts), little is known about the quasi-median generation in Λn starting from a set X of vertices. We describe the vertices of the quasi-median graph generated by X in terms of the coordinatewise partitions of X. In particular, we clarify when the generated quasi-median graph is the so-called relation graph associated with X. This immediately characterizes the instances where either a block graph or the total Hamming graph is generated.