The leafage of a chordal graph
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/9807022,
title = {The leafage of a chordal graph},
author = {In-Jen Lin and Terry A. McKee and Douglas B. West},
journal= {arXiv preprint arXiv:math/9807022},
year = {2007}
}
Comments
19 pages, 3 figures