Polynomial-Time Algorithm for the Leafage of Chordal Graphs

Every chordal graph G can be represented as the intersection graph of a collection of subtrees of a host tree, the so-called tree model of G. The leafage l(G) of a connected chordal graph G is the minimum number of leaves of the host tree of a tree model of G. This concept was first defined by I.-J. Lin, T.A. McKee, and D.B. West in [9]. In this contribution, we present the first polynomial time algorithm for computing l(G) for a given chordal graph G. In fact, our algorithm runs in time O(n3 ) and it also constructs a tree model of G whose host tree has l(G) leaves.

• Type: Conference
• Year: 2009
• Where: ESA
• Authors: Michel Habib, Juraj Stacho
• Keywords: Algorithms, Chordal Graph, ESA 2009, Host Tree, Tree Model