Tree-width of hypergraphs and surface duality

Frédéric Mazoit (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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.

Mots clés: graph; hypergraph; tree-width; duality; surface

Domaines: Mathématique discrète [cs.DM]

Frédéric Mazoit. Tree-width of hypergraphs and surface duality. Journal of Combinatorial Theory, Series B, 2010, 102 (3), pp.671-687. ⟨10.1016/j.jctb.2011.11.002⟩. ⟨hal-00492498v2⟩