Pathwidth of outerplanar graphs

We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected outerplanar graph is at most c plus the pathwidth of its dual. They also conjectured that this was actually true with c being one for every biconnected planar graph. Fomin [10] proved that the second conjecture is true for all planar triangulations. First, we construct for each p ≥ 1 a biconnected outerplanar graph of pathwidth 2p+1 whose (geometric) dual has pathwidth p+1, thereby disproving both conjectures. Next, we also disprove two other conjectures (one of Bodlaender and Fomin [3], implied by one of Fomin [10]). Finally we prove, in an algorithmic way, that the pathwidth of every biconn...

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: David Coudert, Florian Huc, Jean-Sébastien Sereni
• Keywords: Biconnected Outerplanar Graph, Geometric, JGT 2007, Pathwidth