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October 19, 2025Open Access

A perfect matching reciprocity method for embedding multiple hypercubes in an augmented cube: Applications to Hamiltonian decomposition and fault-tolerant Hamiltonicity

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The study establishes a method for embedding hypercubes in augmented cubes, focusing on minimizing common edges.
It proves the presence of edge-disjoint Hamiltonian cycles in augmented cubes, verifying a previous conjecture for odd dimensions.
The results demonstrate fault-tolerant Hamiltonicity for augmented cubes, highlighting their capability to handle faulty edges.
A technique involving reciprocal perfect matchings is utilized, expanding existing knowledge of Cayley properties in graphs.

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This analysis establishes lower bounds for hypercube embeddability in augmented cubes, suggesting new methods for Hamiltonian decomposition.

Yang et al. (2025) studied this question.

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This analysis establishes lower bounds for hypercube embeddability in augmented cubes, suggesting new methods for Hamiltonian decomposition.