Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

A commonly studied means of parameterizing graph problems is the deletion distance from triviality [10], which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known. In the context of graph isomorphism, we define triviality to mean a graph with maximum degree bounded by a constant, as such graph classes admit polynomial-time isomorphism tests. We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions. We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, generalising results of Bouland et al. [2] on isomorphism parameterized by tree-depth.