About Edge Independent Sets in Hypergraphs
نویسندگان
چکیده
منابع مشابه
Independent Sets in Hypergraphs
Many important theorems and conjectures in combinatorics, such as the theorem of Szemerédi on arithmetic progressions and the Erdős-Stone Theorem in extremal graph theory, can be phrased as statements about families of independent sets in certain uniform hypergraphs. In recent years, an important trend in the area has been to extend such classical results to the so-called ‘sparse random setting...
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Given a finite set V , and integers k ≥ 1 and r ≥ 0, denote by A(k, r) the class of hypergraphs A ⊆ 2 with (k, r)-bounded intersections, i.e. in which the intersection of any k distinct hyperedges has size at most r. We consider the problem MIS(A, I): given a hypergraph A and a subfamily I ⊆ I(A), of its maximal independent sets (MIS) I(A), either extend this subfamily by constructing a new MIS...
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The independence number α(H) of a hypergraph H is the size of a largest set of vertices containing no edge of H. In this paper, we prove that if Hn is an n-vertex (r+ 1)-uniform hypergraph in which every r-element set is contained in at most d edges, where 0 < d < n/(logn) 2 , then α(Hn) ≥ cr (n d log n d )1/r where cr > 0 satisfies cr ∼ r/e as r → ∞. The value of cr improves and generalizes se...
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ژورنال
عنوان ژورنال: International Journal of Scientific Research in Mathematical and Statistical Sciences
سال: 2018
ISSN: 2348-4519
DOI: 10.26438/ijsrmss/v5i5.7781