Note: On self-duality of branchwidth in graphs of bounded genus

Authors:
Ignasi Sau;Dimitrios M. Thilikos
Affiliations:
AlGCo group, CNRS, LIRMM, Montpellier, France;Department of Mathematics, National Kapodistrian University of Athens, Greece
Venue:
Discrete Applied Mathematics
Year:
2011

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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 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.