On the generalised colouring numbers of graphs that exclude a fixed minor

In the case of graphs G of bounded genus g, we improve the bounds to colr(G)≤(2g+3)(2r+1) (and even colr(G)≤5r+1 if g=0, i.e. if G is planar) and wcolr(G)≤(2g+r+22)(2r+1).