Geodesic
The leafage of a chordal graph
Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 1, pp. 23-48

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The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n - lg n - 1/2 lg lg n + O(1). The proper leafage l*(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and lower bounds on l*(G). Leafage equals proper leafage on claw-free chordal graphs. We use asteroidal sets and structural properties of chordal graphs.
Keywords: chordal graph, subtree intersection representation, leafage 
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Lin, In-Jen; McKee, Terry; West, Douglas. The leafage of a chordal graph. Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 1, pp. 23-48. http://geodesic.mathdoc.fr/item/DMGT_1998_18_1_a2/