Résumé: If G is an n vertex maximal planar graph and &dgr;?1/3, then the vertex set of G can be partitioned into three sets A, B, C such that neither A nor B contains more than (1-&dgr;)n vertices, no edge from G connects a vertex in A to a vertex in B, and C is a cycle in G containing no more than ('rac'2&dgr;+'rac'2-2&dgr;)'rac'n+O(1) vertices. Specifically, when &dgr; = 1/3, the separator C is of size ('rac'2/3+'rac'4/3)'rac'n+O(1), which is roughly 1.97'rac'n. The constant 1.97 is an improvement over the best known so far result of Miller 2'rac'2 'asympt. equiv.' 2.82. If non-negative weights adding to at most 1 are associated with the vertices of G, then the vertex set of G can be partitioned into three sets A, B, C such that neither A nor B has weight exceeding 1-&dgr;, no edge from G connects a vertex in A to a vertex in B, and C is a simple cycle with no more than 2'rac'n+O(1) vertices.

Langue: Anglais