# FPT algorithm for Partial k-tree Isomorphism

H.L. Bodlander in Polynomial algorithms for graph isomorphism and chromatic index on partial $k$-trees given a polynomial time algorithm for graph isomorphism when $k$ is constant.

Is there any FPT algorithm for partial $k$-tree isomorphism.

• Please note, that the problem is even open for the path / tree distance width and only solved for the rooted tree distance width and some other restrictions (e.g. root sets with c components). The feedback vertex number is another parameter such that $tw\leq f(fvs)$ and for which GI is in FPT (see here, but canonization is open AFAIK). Nov 11, 2013 at 10:21