Complete Partite subgraphs in dense hypergraphs
نویسندگان
چکیده
منابع مشابه
Complete Partite subgraphs in dense hypergraphs
For a given r-uniform hypergraph F we study the largest blow-up of F which can be guaranteed in every large r-uniform hypergraph with many copies of F . For graphs this problem was addressed by Nikiforov, who proved that every n-vertex graph that contains Ω(n`) copies of the complete graph K` must contain a complete `-partite graph with Ω(logn) vertices in each class. We give another proof of N...
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Let r ≥ 3 and (lnn)−1/(r−1) ≤ α ≤ r−3. We show that: Every r-uniform graph on n vertices with at least αnr/r! edges contains a complete r-partite graph with r − 1 parts of size ⌊ α (lnn)1/(r−1) ⌋ and one part of size ⌈ n1−α r−2 ⌉ . This result follows from a more general digraph version: Let U1, . . . , Ur be sets of size n, and M ⊂ U1 × · · · × Ur satisfy |M | ≥ αnr. If the integers s1, . . . ...
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A well-known special case of a conjecture attributed to Ryser (actually appeared in the thesis of Henderson [7]) states that k-partite intersecting hypergraphs have transversals of at most k−1 vertices. An equivalent form of the conjecture in terms of coloring of complete graphs is formulated in [1]: if the edges of a complete graph K are colored with k colors then the vertex set of K can be co...
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Motzkin and Straus established a remarkable connection between the maximum clique and the Lagrangian of a graph in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique number in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we provide upper bounds on the Lagrangian of a hypergr...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2012
ISSN: 1042-9832
DOI: 10.1002/rsa.20441