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The graph isomorphism problem is polynomial

Aleksandr Golubchik
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Abstract

It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties of regular $k$-partitions that, on one hand, generalize automorphic $k$-partitions (=systems of $k$-orbits of permutation groups), and, on other hand, schemes of relations (strongly regular 2-partitions or regular 3-partitions), that are a subject of the algebraic combinatorics. It is shown that the stabilization of a graph by quadrangles detects the triviality of the graph automorphism group. The result is obtained by lineariation of the algebraic combinatorics. Keywords: $k$-partitions, symmetry, algebraic combinatorics

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Aleksandr Golubchik. 2007-05-07. The graph isomorphism problem is polynomial. https://arxiv.org/abs/math/0607770

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