Computing the tree number of a cut-outerplanar graph

Details Computing the tree number of a cut-outerplanar graph Computing the tree number of a cut-outerplanar graph

2009-06-02

arxiv.org/abs/0906.0422v1

Computer Science

Discrete Mathematics

13 pages, 11 figures Main file outerplanar1.tex

Scientific paper

While the notion of arboricity of a graph is well-known in graph theory, very few results are dedicated to the minimal number of trees covering the edges of a graph, called the tree number of a graph. In this paper we propose a method for computing in polynomial time the tree number of a subclass of planar graphs. The subclass in question includes but is not limited to outerplanar graphs; the difference between arboricity and tree number for graphs in this class can be arbitrarily big.

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