A graph class C has polynomial expansion if there is a polynomial function f such that for every graph G is an element of C, each of the depth-r minors of G has average degree at most f (r). In this note, we study bounded-radius variants of some classical graph parameters such as bramble number, linkedness and well-linkedness, and we show that they are pairwise polynomially related. Furthermore, in a graph class with polynomial expansion they are all uniformly bounded by a polynomial in r.
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