Strengthened Dirac-type minimum degree conditions guarantee that the k-switch reconfiguration graphs on perfect matchings are connected and expanders, with matching lower-bound constructions showing exponential numbers of components below certain degree thresholds.
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Dirac's theorem and the switch geometry of perfect matchings
Strengthened Dirac-type minimum degree conditions guarantee that the k-switch reconfiguration graphs on perfect matchings are connected and expanders, with matching lower-bound constructions showing exponential numbers of components below certain degree thresholds.