Non-Hamiltonian 2-regular Digraphs -- Residues
Combinatorics
2026-01-27 v1
Abstract
In earlier papers, we showed a decomposition of the arcs of 2-diregular digraphs (2-dds) and used it to prove some conditions for these graphs to be non-Hamiltonian; we then extended this decomposition to a larger class of digraphs and used it to construct infinite families of (strongly) connected non-Hamiltonian 2-dds and provided techniques to establish non-Hamiltonicity in special cases. In the present paper, for a subclass of these graphs, we show connections between non-Hamiltonicity and sets of permutations in the full symmetric group S(n) by introducing the concepts of biconjugates, excluded sets and residues; we then use these concepts to prove a necessary and sufficient condition for non-Hamiltonicity.
Cite
@article{arxiv.2601.17177,
title = {Non-Hamiltonian 2-regular Digraphs -- Residues},
author = {Munagala V. Ramanath},
journal= {arXiv preprint arXiv:2601.17177},
year = {2026}
}