On self duality of pathwidth in polyhedral graph embeddings

: Let G be a 3-connected planar graph and G∗ be its dual. We show that the pathwidth of G∗ is at most 6 times the pathwidth of G. We prove this result by relating the pathwidth of a graph with the cut-width of its medial graph and we extend it to bounded genus embeddings. We also show that there exist 3-connected planar graphs such that the pathwidth

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: Fedor V. Fomin, Dimitrios M. Thilikos
• Keywords: 3-connected Planar Graphs, JGT 2007, Medial Graph, Pathwidth