O-joung Kwon (권오정), Mim-width: a width parameter beyond rank-width

Vatshelle (2012) introduced a width parameter called mim-width. It is based on the following cut function : for a vertex partition (A,B) of a graph, the complexity of this partition is computed by the size of a maximum induced matching of the bipartite subgraph induced by edges between A and B. This parameter naturally extends the expressibility power of the graph parameters clique-width and rank-width, which have been well-developed in recent years. In a series of papers, we explored the computational complexity of several problems, parameterized by mim-width. We summarize known structural properties and algorithmic applications of mim-width, and give some open problems at the end. This is joint work with Lars Jaffke, Torstein Strømme, and Jan Arne Telle.