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The leafage of a chordal graph

In-Jen Lin·Terry A. McKee·Douglas B. West
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Abstract

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.

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In-Jen Lin, Terry A. McKee, Douglas B. West. 1998-07-03. The leafage of a chordal graph. https://arxiv.org/abs/math/9807022

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