# On classes of graphs with strongly sublinear separators

For real numbers c,epsilon>0, let G_c,epsilon denote the class of graphs G such that each subgraph H of G has a balanced separator of order at most c|V(H)|^1-epsilon. A class of graphs has strongly sublinear separators if it is a subclass of G_c,epsilon for some c,epsilon>0. We investigate properties of such graph classes, leading in particular to an approximate algorithm to determine membership in G_c,epsilon: there exist c'>0 such that for each input graph G, this algorithm in polynomial time determines either that G belongs to G_c',epsilon^2/160, or that G does not belong to G_c,epsilon.

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