Sublinear separators, fragility and subexponential expansion

Abstract

Let g be a subgraph-closed graph class with bounded maximum degree. We show that if g has balanced separators whose size is smaller than linear by a polynomial factor, then g has subexponential expansion.

This gives a partial converse to a result of Nesetril and Ossona de Mendez. As an intermediate step, the proof uses a new kind of graph decompositions.

Keywords

• tree-width
• planar graphs
• theorem
• minors
• sparsification
• completeness