On self-duality of branchwidth in graphs of bounded genus

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 by 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 image for any graph image embedded in a surface of Euler genus image.