On One-factorization of Complete 3-Uniform Hypergraphs
نویسندگان
چکیده
A hypergraph H on n nodes is complete 3-uniform if the hyperedges are precisely the set of all node triples. A one-factor of H is a set of hyperedges that cover each node exactly once. According to Baranyai's proof, the hyperedges of H can be partitioned into one-factors iff n ≡ 0 (mod 3). Though the proof is constructive, it leads to an O(2)-time algorithm. We investigate a method for computing one-factorization of a complete 3-uniform hypergraph, which finds a representative set of one-factors, from which the remaining factors are obtained by cyclic permutation of the hyperedge end-nodes. Such one-factorization is utilized in parallel algorithms for tightening inter-atomic distance bounds for the molecular conformation problem.
منابع مشابه
Embedding Factorizations for 3-Uniform Hypergraphs II: $r$-Factorizations into $s$-Factorizations
Motivated by a 40-year-old problem due to Peter Cameron on extending partial parallelisms, we provide necessary and sufficient conditions under which one can extend an r-factorization of a complete 3-uniform hypergraph on m vertices, K3 m, to an s-factorization of K3 n. This generalizes an existing result of Baranyai and Brouwer–where they proved it for the case r = s = 1.
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