A Dyck-word tree that controls all odd graphs

Italo J. Dejter

Published 2023-06-25Version 1

An infinite ordered tree $T$ exists that has as its vertex set a collection of tight restricted-growth strings representing all Dyck words; these stand for the cyclic (resp., dihedral) classes and uniform 2-factor cycles of odd graphs (resp., middle-levels graphs). Odd graphs have edge-supplementary arc-factorizations based on Dyck words which, represented as Dyck nests, possess a signature admitting universal updates along $T$ and allowing an arc-factorization view of the Hamilton cycles found by T. M\"utze et al.