Embedding Factorizations for 3-Uniform Hypergraphs
نویسندگان
چکیده
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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Chvátal, Rödl, Szemerédi and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [6, 23] the same result was proved for 3-uniform hypergraphs. Here we extend this result to k-uniform hypergraphs for any integer k ≥ 3. As in the 3-uniform case, the main new tool which we prove and use is an embedding lemma for k-uniform hypergraphs of boun...
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Chvátal, Rödl, Szemerédi and Trotter [1] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform ‘pseudo-random’ hypergraphs. keywords: hypergraphs; regularity lemm...
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Chvátal, Rödl, Szemerédi and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [5, 19] the same result was proved for 3-uniform hypergraphs. Here we extend this result to k-uniform hypergraphs for any integer k ≥ 3. As in the 3-uniform case, the main new tool which we prove and use is an embedding lemma for k-uniform hypergraphs of boun...
متن کاملOn the numbers of 1-factors and 1-factorizations of hypergraphs
A hypergraph G = (X,W ) is called d-uniform if each hyperedge w is a set of d vertices. A 1-factor of a hypergraph G is a set of hyperedges such that every vertex of the hypergraph is incident to exactly one hyperedge from the set. A 1factorization of G is a partition of all hyperedges of the hypergraph into disjoint 1-factors. The adjacency matrix of a d-uniform hypergraph G is the d-dimension...
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 73 شماره
صفحات -
تاریخ انتشار 2013