Vertex-minor reductions can simulate edge contractions

We prove that local complementation and vertex deletion, operations from which vertexminors are defined, can simulate edge contractions. As an application, we prove that the rank-width of a graph is linearly bounded in term of its tree-width. Key words: Clique-width, rank-width, tree-width, tree-decomposition, local complementation, edge contraction, vertex-minor.

• Type: Journal
• Year: 2007
• Where: DAM
• Authors: Mamadou Moustapha Kanté
• Keywords: DAM 2007, Edge, Local Complementation, Vertex Deletion