On classes of graphs with strongly sublinear separators. (June 2018) - Dvořák, Zdeněk
Abstract: For real numbers c, ε > 0, let G c, ε 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 − ε . A class G of graphs has strongly sublinear separators if G ⊆ G c, ε for some c, ε > 0 . We investigate properties of such graph classes, leading in particular to an approximate algorithm to determine membership in G c, ε : there exist c ′ > 0 such that for each input graph G, this algorithm in polynomial time determines either that G ∈ G c ′, ε 2 ∕ 160, or that G ∉ G c, ε .