k-separator chordal graphs: leafage and subfamilies

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Abstract

The leafage of a chordal graph G is the minimum number of leaves among the clique-trees of G. In this paper, based on properties of the minimal vertex separators, the leafage of a k-separator chordal graph is determined in linear time. This result allows establishment of the relationship of some subfamilies of chordal graphs, such as k-trees, interval and uniquely representable chordal graphs.

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