On the Sizes of Vertex-k-Maximal r-Uniform Hypergraphs
نویسندگان
چکیده
منابع مشابه
On the Inapproximability of Vertex Cover on k-Partite k-Uniform Hypergraphs
Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. While intractable in general, it is well known that on bipartite graphs, vertex cover is polynomial time solvable. In this work, we study the natural extension of bipartite vertex cover to hypergraphs, namely finding a small vertex cover in kuniform k-partite hypergraphs, when the k-partition is gi...
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In 1965 Motzkin and Straus established a remarkable connection between the local/global maximizers of the Lagrangian of a graph G over the standard simplex ∆ and the maximal/maximum cliques of G. In this work we generalize the Motzkin-Straus theorem to k-uniform hypergraphs, establishing an isomorphism between local/global minimizers of a particular function over ∆ and the maximal/maximum cliqu...
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We study the problem of computing the minimum vertex cover on k-uniform k-partite hypergraphs when the k-partition is given. On bipartite graphs (k = 2), the minimum vertex cover can be computed in polynomial time. For k ≥ 3, this problem is known to be NP-hard. For general k, the problem was studied by Lovász [23], who gave a k2 -approximation based on the standard LP relaxation. Subsequent wo...
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We study the problem of computing the minimum vertex cover on k-uniform k-partite hypergraphs when the k-partition is given. On bipartite graphs (k = 2), the minimum vertex cover can be computed in polynomial time. For general k, the problem was studied by Lovász [23], who gave a k 2 -approximation based on the standard LP relaxation. Subsequent work by Aharoni, Holzman and Krivelevich [1] show...
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In this paper we examine the orders of vertex-transitive self-complementary uniform hypergraphs. In particular, we prove that if there exists a vertex-transitive selfcomplementary k-uniform hypergraph of order n, where k = 2 or k = 2 + 1 and n ≡ 1 (mod 2), then the highest power of any prime dividing n must be congruent to 1 modulo 2. We show that this necessary condition is also sufficient in ...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2019
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-019-02052-z