Rank‐width is less than or equal to branch‐width
Sang‐il Oum · Journal of Graph Theory · 2007
Abstract We prove that the rank‐width of the incidence graph of a graph G is either equal to or exactly one less than the branch‐width of G, unless the maximum degree of G is 0 or 1. This implies that rank‐width of a graph is less than or equal to branch‐width of the graph unless the branch‐width is 0. Moreover, this inequality is tight. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 239–244, 2008