English

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

R2 v1 2026-07-22T17:59:11.859Z