Abstract of

Abstract: Treewidth and duality for planar hypergraphs.

by Denis Lapoire

We prove a conjecture of Robertson and Seymour (Graph Minors.~{III}. Planar tree-width): the treewidth of a planar graph is at most the treewidth of its dual plus one. To this purpose, we study hypermaps, which represent hypergraphs on a surface. We define a parallel composition on hypermaps which verifies five properties: it is commutative, associative, preserves planarity, commutes with the duality and with the parallel composition on hypergraphs. Finally, we introduce the notion of a equationel set of hypermaps and of a treewidth of a hypermap.