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The complexity of graph isomorphism (GraphIso) is a famous unresolved problem in theoretical computer science. For graphs G and H, it asks whether they are the same up to a relabeling of vertices. In 1981, Lubiw proved that list restricted graph isomorphism (ListIso) is NP-complete: for each u ∈ V(G), we are given a list L(u) ⊆ V(H) of possible images of u. After 35 years, we revive the study of this problem and consider which results for GraphIso translate to ListIso. We prove the following:arXiv:1607.03918v2 fatcat:rea4gbmazrbebbirsyhndky7mu