Non-Hamiltonian 2-regular Digraphs -- Residues
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917220388438016 |
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| 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 |
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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 |