Graph isomorphism restricted by lists

Abstract The complexity of graph isomorphism ( GraphIso ) is a famous problem in computer science. For graphs G and H, it asks whether they are the same up to relabeling vertices. In 1981, Lubiw proved that list restricted ListIso NP -complete: for each u ∈ V , we given L ⊆ H possible images u. After 35 years, revive study this consider which results can be modified solve . We prove: 1) Under certain conditions, GI -completeness class implies 2) Several combinatorial algorithms : trees, planar graphs, interval circle permutation bounded treewidth graphs. 3) -complete cubic colored with sizes color classes by 8 all lists size at most 3.