For each k≥4, an explicit construction maps a finite compatible-choice system to two equal-size simple uncolored graphs that are k-dimensional Weisfeiler–Leman equivalent exactly when the system has no successful choice; a successful choice is detected after two joint-refinement rounds or one separate-refinement round.
For each k≥4, an explicit construction maps a finite compatible-choice system to two equal-size simple uncolored graphs that are k-dimensional Weisfeiler–Leman equivalent exactly when the system has no successful choice; a successful choice is detected after two joint-refinement rounds or one separate-refinement round.
For each k≥4, an explicit construction maps a finite compatible-choice system to two equal-size simple uncolored graphs that are k-dimensional Weisfeiler–Leman equivalent exactly when the system has no successful choice; a successful choice is detected after two joint-refinement rounds or one separate-refinement round.
If correct, gives a direct reduction from simultaneous finite choices to bounded-dimension graph refinement.
Can compatible finite-domain choices be encoded exactly as early k-dimensional Weisfeiler–Leman distinction of uncolored graphs?
Publication dates and editorial changes.
OpenAI reports a parity-lift reduction for Weisfeiler–Leman equivalence
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