A subfamily of Dyck words called tight Dyck words is seen to correspond, via a “castling” procedure, to the vertex set of an ordered tree T. From T, a “blowing” operation recreates the whole family ol Dyck words. The vertices of T can be elementarily updated all along T. This simplifies an edge-supplementary arc-factorization view of Hamilton cycles of odd and middle-levels graphs found by T. Mütze et al. This takes into account that the Dyck words represent: (a) the cyclic and dihedral vertex classes of odd and middle-levels graphs, respectively, and (b) the cycles of their 2-factors, as found by T. Mütze et al.
