Intersection dimensions of graph classes (Q1334942)

``The intersection dimension of a graph \(G\) with respect to a class \(A\) of graphs is the minimum \(k\) such that \(G\) is the intersection of at most \(k\) graphs on vertex set \(V(G)\) each of which belongs to \(A\). We consider the question when the intersection dimension of a certain family of graphs is bounded or unbounded.'' If \(A\) is hereditary and does not contain all graphs, then the intersection dimension of all graphs with respect to \(A\) is unbounded. The intersection dimension of planar graphs with respect to permutation graphs is bounded.