$\mathbb F$ -Rank-Width of (Edge-Colored) Graphs

摘要: Rank-width is a complexity measure equivalent to the clique-width of undirected graphs and has good algorithmic structural properties. It in particular related vertex-minor relation. We discuss an extension notion rank-width all types - directed or not, with edge colors not -, named \(\mathbb F\)-rank-width. extend most results known for F\)-rank-width graphs: cubic-time recognition algorithm, characterisation by excluded configurations under pivot-minor, algebraic graph operations. also show that special case