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 that given a hypergraph H on a surface of Euler genus k, the tree-width of H^∗ is at most the maximum of tw(H)+1+k and the maximum size of a hyperedge of H^∗ minus one.

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

Domaines: Mathématique discrète [cs.DM]

Frédéric Mazoit. Tree-width of hypergraphs and surface duality. 2010. ⟨hal-00492498v1⟩