An efficient algorithm to recognize locally equivalent graphs


To locally complement a simple graphF at one of its verticesv is to replace the subgraph induced byF onn(v)={w:vw is an edge ofF} by the complementary subgraph. Graphs related by a sequence of local complementations are said to be locally equivalent. We associate a system of equations with unknowns inGF(2) to any pair of graphs {F, F′}, so thatF is locally equivalent toF′ if and only if the system has a solution. The equations are either linear and homogenous or bilinear, and we find a solution, if any, in polynomial time.

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With partial support of P. R. C. Mathématiques et Informatique.

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Bouchet, A. An efficient algorithm to recognize locally equivalent graphs. Combinatorica 11, 315–329 (1991).

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  • 05C