image-join decomposable graphs and algorithms with runtime single exponential in rankwidth Original Research Article

We introduce image-join decompositions of graphs, indexed by a fixed bipartite graph image. These decompositions are based on a graph operation that we call a image-join, which adds edges between two given graphs by taking partitions of their two vertex sets, identifying the classes of the partitions with vertices of image, and connecting classes by the pattern image. image-join decompositions are related to modular, split and rank decompositions.