The Rank-Width of the Square Grid
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Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
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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