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arXiv · 2601.17177

Non-Hamiltonian 2-regular Digraphs -- Residues

Munagala V. Ramanath
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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.

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Munagala V. Ramanath. 2026-01-23. Non-Hamiltonian 2-regular Digraphs -- Residues. https://arxiv.org/abs/2601.17177

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