Isomorphism for Graphs of Bounded Feedback Vertex Set Number [chapter]

Stefan Kratsch, Pascal Schweitzer
2010 Lecture Notes in Computer Science  
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 2 ), 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
more » ... tion rules that produce an isomorphism-invariant outcome, interleaved with the creation of increasingly large partial isomorphisms.
doi:10.1007/978-3-642-13731-0_9 fatcat:ys6cnyk3qfaatfczzh24vkxlvm