A graph parameter is self-dual in some class of graphs embeddable in some surface if its value does not change in the dual graph more than a constant factor. Self-duality has been examined for several width-parameters, such as branchwidth, pathwidth, and treewidth. In this paper, we give a direct proof of the self-duality of branchwidth in graphs embedded in some surface. In this direction, we prove that bw(G ∗ ) ≤ 6 · bw(G) + 2g − 4 for any graph G embedded in a surface of Euler genus g
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