Castling tree of tight Dyck nests with applications to odd and middle-levels graphs
Abstract
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. M\"utze et al. This take into account that the Dyck words represent: {\bf(a)} the cyclic and dihedral vertex classes of odd and middle-levels graphs, respectively, and {\bf(b)} the cycles of their 2-factors, as found by T. M\"utze et al.
Fields of Study & Subjects
Computational Geometry and Mesh Generation
Advanced Graph Theory Research
Publication details
- Journal / source
- Open Journal of Discrete Applied Mathematics
- Publisher
- Ptolemy Scientific Research Press
- Volume
- 9
- Issue
- 1
- Pages
- 9–29
- Publication date
- 10 April 2026
- Language
- EN