Geelen's simulation conjecture for vertex-minor-closed graph classes

From papers

A graph class is vertex-minor-closed if it contains every vertex-minor of each of its graphs. Geelen's simulation conjecture. Measurement-based quantum computation (MBQC) is efficiently classically simulable on every vertex-minor-closed class of graphs other than the class of all graphs. The conjecture is known for circle graphs and for graphs of bounded rank-width, but remains open for arbitrary vertex-minor-closed classes.

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Sources & referencesView supporting material

Primary source

Frederik Hahn, Rose McCarty, Hendrik Poulsen Nautrup and Nathan Claudet, “The Structure of Circle Graph States”, arXiv:2603.08847 (2026).

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