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1998 | 18 | 1 | 23-48
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The leafage of a chordal graph

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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.
Opis fizyczny
  • National Ocean University, Taipei, Taiwan
  • Wright State University, Dayton, OH 45435-0001, U.S.A
  • University of Illinois, Urbana, IL 61801-2975, U.S.A.
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