Two graph isomorphism polytopes
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The convex hull @j"n","n of certain (n!)^2 tensors was considered recently in connection with graph isomorphism. We consider the convex hull @j"n of the n! diagonals among these tensors. We show: 1. The polytope @j"n is a face of @j"n","n. 2. Deciding if a graph G has a subgraph isomorphic to H reduces to optimization over @j"n. 3. Optimization over @j"n reduces to optimization over @j"n","n. In particular, this implies that the subgraph isomorphism problem reduces to optimization over @j"n","n.
[1] Shmuel Onn,et al. Geometry, Complexity, and Combinatorics of Permutation Polytopes , 1993, J. Comb. Theory A.
[2] Shmuel Friedland,et al. On the graph isomorphism problem , 2008, ArXiv.