Branchwidth is (1,g)-self-dual

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. We prove that the branchwidth of connected hypergraphs without bridges and loops that are embeddable in some surface of Euler genus at most g is an (1,g)-self-dual parameter. This is the first proof that branchwidth is an additively self-dual width parameter.Comment: 10 page

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 bw(G*)≤6·bw(G)+2g-4 for any graph G embedded in a surface of Euler genus g. © 2011 Elsevier B.V. All rights reserved

On self-duality of branchwidth in graphs of bounded genus

International audienceA 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 bw(G*) < 6bw(G)+2g-3 for any graph G embedded in a surface of Euler genus g