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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.21381 |
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| _version_ | 1866912507819458560 |
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| author | Ramanath, Munagala V. S. |
| author_facet | Ramanath, Munagala V. S. |
| contents | In earlier papers, we showed a decomposition of 2-diregular digraphs (2-dds) and used it to provide some sufficient conditions for these graphs to be non-Hamiltonian; we also showed a close connection between the permanent and determinant of the adjacency matrices of these digraphs and gave some enumeration and generation results. In the present paper we extend the discussion to a larger class of digraphs, introduce the notions of routes and quotients and use them to provide additional criteria for 2-dds to be non-Hamiltonian. Though individual non-Hamiltonian regular connected graphs of low degree are known (e.g. Tutte and Meredith graphs), families of such graphs are not common in the literature; even scarcer are families of such digraphs. Our results identify a few such families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Hamiltonian 2-regular Digraphs Ramanath, Munagala V. S. Combinatorics 05 In earlier papers, we showed a decomposition of 2-diregular digraphs (2-dds) and used it to provide some sufficient conditions for these graphs to be non-Hamiltonian; we also showed a close connection between the permanent and determinant of the adjacency matrices of these digraphs and gave some enumeration and generation results. In the present paper we extend the discussion to a larger class of digraphs, introduce the notions of routes and quotients and use them to provide additional criteria for 2-dds to be non-Hamiltonian. Though individual non-Hamiltonian regular connected graphs of low degree are known (e.g. Tutte and Meredith graphs), families of such graphs are not common in the literature; even scarcer are families of such digraphs. Our results identify a few such families. |
| title | Non-Hamiltonian 2-regular Digraphs |
| topic | Combinatorics 05 |
| url | https://arxiv.org/abs/2507.21381 |