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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r-regular digraphs satisfy c(D) >= ceil(3r/22) with an improved upper bound, and have directed tree-width Omega(r), yielding corollaries on cylindrical wall subdivisions.
citing papers explorer
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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.
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Openly disjoint cycles and directed tree-width of regular digraphs
r-regular digraphs satisfy c(D) >= ceil(3r/22) with an improved upper bound, and have directed tree-width Omega(r), yielding corollaries on cylindrical wall subdivisions.