On the sizes of (k,l)-edge-maximal r-uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Uniform Edge Distribution in Hypergraphs is Hereditary
Let α ∈ (0, 1), l ≥ 2 and let Hn be an l-graph on n vertices. Hn is (α, ξ)-uniform if every ξn vertices of Hn span (α± ξ) ( ξn l ) edges. Our main result is the following. For all δ̃, there exist δ, r, n0 such that, if n > n0 and H n is (α, δ)-uniform, then all but exp{−r/20} ( n r ) r-sets of vertices induce a subhypergraph that is (α, δ̃)-uniform. We also present the following application. Let ...
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The degree of an edge e in a hypergraph G is the number of other edges of G intersecting e, and the maximum edge degree of G is the maximum over the degrees of its edges. A natural question is: Which bound on the maximum edge degree of an r-uniform hypergraph G provides that G is k-colorable? The classical result in this direction belongs to Erdős and Lovász. In their seminal paper [2] (where t...
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Denote by Ω = {1, . . . , n} an n–element set. For all A,B ∈ Ωk ) , the k–element subsets of Ω, define the relation ∼ as follows: A ∼ B iff A and B have a common shadow, i.e. there is a C ∈ ( Ω k−1 ) with C ⊂ A and C ⊂ B. For fixed integer α, our goal is to find a family A of k–subsets with size α, having as many as possible ∼ –relations for all pairs of its elements. For k = 2 this was achieve...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2020
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2362