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On the Path-Width of Planar Graphs.

SIAM J. Discrete Math 01/2009; 23:1311-1316. DOI: 10.1137/060670146
Source: DBLP

ABSTRACT In this paper, we present a result concerning the relation between the path-with of a planar graph and the path-width of its dual. More precisely, we prove that for a 3-connected planar graph G, pw(G) 3pw(G ) + 2. For 4-connected planar graphs, and more generally for Hamiltonian planar graphs, we prove a stronger bound pw(G ) 2 pw(G) + c. The best previously known bound was obtained by Fomin and Thilikos who proved that pw(G ) 6 pw(G) + cte. The proof is based on an algorithm which, given a xed spanning tree of G, transforms any given decomposition of G into one of G. The ratio of the corresponding parameters is bounded by the maximum degree of the spanning tree.

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