Publication at Faculty of Mathematics and Physics |
2018
Abstract
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 vertical bar V(H)vertical bar(1-epsilon). A class g of graphs has strongly sublinear separators if G subset 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 is an element of G(c',epsilon 2/160), or that G is not an element of G(c,epsilon).