Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.17177 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917220388438016 |
|---|---|
| author | Ramanath, Munagala V. |
| author_facet | Ramanath, Munagala V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17177 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Hamiltonian 2-regular Digraphs -- Residues Ramanath, Munagala V. Combinatorics 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. |
| title | Non-Hamiltonian 2-regular Digraphs -- Residues |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.17177 |