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 c...

Abstract We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and Yaacov, Doucha, Nies, Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences the perturbation systems former paper, such as Banach‐Mazur distance Lipschitz between metric spaces. Our is characterized syntacticall...

The convex hull ψn,n of certain (n!) 2 tensors was considered recently in connection with graph isomorphism. We consider the convex hull ψn of the n! diagonals among these tensors. We show: 1. The polytope ψn is a face of ψn,n. 2. Deciding if a graph G has a subgraph isomorphic to H reduces to optimization over ψn. 3. Optimization over ψn reduces to optimization over ψn,n. In particular, this i...

In this work a convex relaxation of a subgraph isomorphism problem is proposed, which leads to a new lower bound that can provide a proof that a subgraph isomorphism between two graphs can not be found. The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail. We consider subgraph isomorphism prob...