Abstract.
We prove that for every 2-connected planar graph the pathwidth of its geometric dual is less than the pathwidth of its line graph. This implies that pathwidth(H)≤ pathwidth(H *)+1 for every planar triangulation H and leads us to a conjecture that pathwidth(G)≤pathwidth(G *)+1 for every 2-connected graph G.
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Received: May 8, 2001 Final version received: March 26, 2002
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ID="*" I acknowledge support by EC contract IST-1999-14186, Project ALCOM-FT (Algorithms and Complexity - Future Technologies) and support by the RFBR grant N01-01-00235.
Acknowledgments. I am grateful to Petr Golovach, Roland Opfer and anonymous referee for their useful comments and suggestions.
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Fomin, F. Pathwidth of Planar and Line Graphs. Graphs and Combinatorics 19, 91–99 (2003). https://doi.org/10.1007/s00373-002-0490-z
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DOI: https://doi.org/10.1007/s00373-002-0490-z