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On the Pathwidth of Planar Graphs

Omid Amini 1 Florian Huc 1 Stéphane Pérennes 1
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : 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.
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Submitted on : Friday, July 7, 2006 - 3:56:20 PM
Last modification on : Friday, February 4, 2022 - 3:12:31 AM
Long-term archiving on: : Monday, April 5, 2010 - 11:25:28 PM


  • HAL Id : inria-00082035, version 1



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



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