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 ) . (The Burr–Erdős conjecture relates to ∇ 0 ( G ) .) This implies the linearity of the Ramsey number and the bounded game chromatic number for some new classes of graphs.