Constructing Hamiltonian Decompositions of Complete $k$-Uniform Hypergraphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909594481065984 |
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| author | Maheri, Javad Elia, Petros |
| author_facet | Maheri, Javad Elia, Petros |
| contents | Motivated by the wide-ranging applications of Hamiltonian decompositions in distributed computing, coded caching, routing, resource allocation, load balancing, and fault tolerance, our work presents a comprehensive design for Hamiltonian decompositions of complete $k$-uniform hypergraphs $K_n^k$. Building upon the resolution of the long-standing conjecture of the existence of Hamiltonian decompositions of complete hypergraphs, a problem that was resolved using existence-based methods, our contribution goes beyond the previous explicit designs, which were confined to the specific cases of $k=2$ and $k=3$, by providing explicit designs for all $k$ and $n$ prime, allowing for a broad applicability of Hamiltonian decompositions in various settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18434 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing Hamiltonian Decompositions of Complete $k$-Uniform Hypergraphs Maheri, Javad Elia, Petros Information Theory Motivated by the wide-ranging applications of Hamiltonian decompositions in distributed computing, coded caching, routing, resource allocation, load balancing, and fault tolerance, our work presents a comprehensive design for Hamiltonian decompositions of complete $k$-uniform hypergraphs $K_n^k$. Building upon the resolution of the long-standing conjecture of the existence of Hamiltonian decompositions of complete hypergraphs, a problem that was resolved using existence-based methods, our contribution goes beyond the previous explicit designs, which were confined to the specific cases of $k=2$ and $k=3$, by providing explicit designs for all $k$ and $n$ prime, allowing for a broad applicability of Hamiltonian decompositions in various settings. |
| title | Constructing Hamiltonian Decompositions of Complete $k$-Uniform Hypergraphs |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.18434 |