Reinterpreting the middle-levels theorem via natural enumeration of ordered trees
Italo Jose Dejter · Open Journal of Discrete Applied Mathematics · 2020
Let 0 < k ∈ Z.A reinterpretation of the proof of existence of Hamilton cycles in the middle-levels graph M k induced by the vertices of the (2k + 1)-cube representing the kand (k + 1)-subsets of {0, . . ., 2k} is given via an associated dihedral quotient graph of M k whose vertices represent the ordered (rooted) trees of order k + 1 and size k.