A characterization for a set of partial partitions to define an X-tree

Authors:
Charles Semple;Mike Steel
Affiliations:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zeland;Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zeand
Venue:
Discrete Mathematics
Year:
2002

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Abstract

Trees whose vertices are partially labelled by elements of a finite set X provide a natural way to represent partitions of subsets of X. The condition under which a given collection of such partial partitions of X can be represented by a tree has previously been characterized in terms of a chordal graph structure on an underlying intersection graph. In this paper, we obtain a related graph-theoretic characterization for the uniqueness of a tree representation of a set of partial partitions of X.