Fraternal augmentations, arrangeability and linear Ramsey numbers

We relate the notions of arrangeability and admissibility to bounded expansion classes and prove that these notions can be characterized by ∇1(G)∇1(G). (The Burr–Erdős conjecture relates to ∇0(G)∇0(G).) This implies the linearity of the Ramsey number and the bounded game chromatic number for some new classes of graphs.