Tree-width of hypergraphs and surface duality

Authors:
Frédéric Mazoit
Affiliations:
Univ. Bordeaux, LaBRI, 351, cours de la Libération, F-33405 Talence cedex, France
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

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Abstract

In Graph minors III, Robertson and Seymour write: ''It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal - indeed, we have convinced ourselves that they differ by at most one.'' They never gave a proof of this. In this paper, we prove a generalisation of this statement to embedding of hypergraphs on general surfaces, and we prove that our bound is tight.