On the Pathwidth of Planar Graphs

@inproceedings{Amini2005OnTP,
  title={On the Pathwidth of Planar Graphs},
  author={Omid Amini and Florian Huc and St{\'e}phane P{\'e}rennes},
  year={2005}
}
Fomin and Thilikos in [5] conjectured that there is a constant $c$ such that, for every $2$-connected planar graph $G$, {pw}(G^*) \leq 2\text{pw}(G)+c$ (the same question was asked simutaneously by Coudert, Huc and Sereni in [4]). By the results of Boedlander and Fomin [2] this holds for every outerplanar graph and actually is tight by Coudert, Huc and Sereni [4]. In [5], Fomin and Thilikos proved that there is a constant $c$ such that the pathwidth of every 3-connected graph $G$ satisfies… CONTINUE READING