On the Pathwidth of Planar Graphs

Omid Amini (1) , Florian Huc (1) , Stéphane Pérennes (1)

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications

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: ${pw}(G^*) \leq 6\text{pw}(G)+c$. In this paper we improve this result by showing that the dual a 3-connected planar graph has pathwidth at most $3$ times the pathwidth of the primal plus two. We prove also that the question can be answered positively for $4$-connected planar graphs.

Domaines: Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]

Omid Amini, Florian Huc, Stéphane Pérennes. On the Pathwidth of Planar Graphs. [Research Report] 2006, pp.6. ⟨inria-00082035⟩