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.Comment: 19 pages, 3 figure
