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A bipartite 2-regular graph is a bipartite graph \(G\) such that \(G = C_{2n₁} ∪ C_{2n₂} ∪ ⋯ ∪ C_{2nₖ}\) with \(k ≥ 1\), i.e., \(G\) is a vertex-disjoint union of bipartite cycles. In this paper, we completely characterize the bipartite 2-regular graphs which can be uniquely bi-embedded into their bipartite complements.
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Wang et al. (2026) studied this question.
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