Tree-width of hypergraphs and surface duality

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.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Frédéric Mazoit
• Keywords: CORR 2008, Education, Graph Minors, Planar Graph, Tree-width