Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
Isotropic matroids II: Circle graphs
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abstract
We present several characterizations of circle graphs, which follow from Bouchet's circle graph obstructions theorem.
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The Structure of Circle Graph States
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.