Graph isomorphism parameterized by feedback vertex set number is fixed-parameter tractable

We prove that the Graph Isomorphism problem is fixed-parameter tractable when parameterized by the feedback vertex set number. That parameter is defined as the number of vertex deletions required to obtain a forest. For graphs of bounded feedback vertex set number the presented algorithm runs in time O(n), and is thereby the first fixed-parameter tractable Graph Isomorphism algorithm for a non-trivial parameter. Central to the algorithm is a new technique consisting of an application of reduction rules that produce an isomorphism-invariant outcome, interleaved with the creation of increasingly large partial isomorphisms.