A characterization for a set of partial partitions to define an X-tree
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.
SubjectsField of Research::01 - Mathematical Sciences::0101 - Pure Mathematics::010101 - Algebra and Number Theory
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