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October 5, 2025Journal of Interconnection Networks

On Extension of Matchings to Hamiltonian Cycles in 6-Cubes

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Every matching consisting of up to 20 edges in the 6-dimensional hypercube can be extended to a Hamiltonian cycle.
All perfect matchings in the hypercube are extendable to Hamiltonian cycles, demonstrating a robust connection.
Wang and Zhao's earlier results affirmed that every matching can achieve this extension in the 6-cube.
This work builds upon previous findings, confirming the extension property across a wider range of matchings.

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Implication

This analysis shows that every matching in a 6-dimensional hypercube can be extended to a Hamiltonian cycle, highlighting its significance in combinatorial mathematics.

Cite This Study

Ali et al. (2025) studied this question.

synapsesocial.com/papers/68e25382d6d66a53c24749cd https://doi.org/10.1142/s0219265925500227

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Implication

This analysis shows that every matching in a 6-dimensional hypercube can be extended to a Hamiltonian cycle, highlighting its significance in combinatorial mathematics.

On Extension of Matchings to Hamiltonian Cycles in 6-Cubes

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Implication

Cite This Study

On Extension of Matchings to Hamiltonian Cycles in 6-Cubes

Key Points

Discussion

Implication

Cite This Study

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