On Self-Duality of Branchwidth in Graphs of Bounded Genus
Abstract
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 in graphs in some surface. In this direction, we prove that $\\mathbf bw(G^*) \\leq 6\\times \\mathbf bw(G) +2g-4$ for any graph $G$ embedded in a surface of Euler genus $g$.