Model Checking on Interpretations of Classes of Bounded Local Cliquewidth

Abstract

An interpretation is an operation that maps an input graph to an output graph by redefining its edge relation using a first-order formula. This rich framework includes operations such as taking the complement or a fixed power of a graph as (very) special cases. We prove that there is an FPT algorithm for the first-order model checking problem on classes of graphs which are first-order interpretable in classes of graphs with bounded local cliquewidth. Notably, this includes interpretations of planar graphs, and of classes of bounded genus in general. To obtain this result we develop a new tool which works in a very general setting of NIP classes and which we believe can be an important ingredient in obtaining similar results in the future.