Abstract
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(n 3) and it also constructs a tree model of G whose host tree has l(G) leaves.
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Habib, M., Stacho, J. (2009). Polynomial-Time Algorithm for the Leafage of Chordal Graphs. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_27
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DOI: https://doi.org/10.1007/978-3-642-04128-0_27
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