DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory  18(1) (1998)   23-48
DOI: 10.7151/dmgt.1061

THE LEAFAGE OF A CHORDAL GRAPH

In-Jen Lin
National Ocean University, Taipei, Taiwan

Terry A. McKee
Wright State University, Dayton, OH 45435-0001, U.S.A

Douglas B. West
University of Illinois, Urbana, IL 61801-2975, U.S.A.

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 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.

1991 Mathematics Subject Classification: 05C75, 05C05, 05C35.

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Received 2 January 1997
Revised 19 April 1998