On vertex independence number of uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
A note on the Caro-Tuza bound on the independence number of uniform hypergraphs
We show some consequences of Caro and Tuza’s [J. Graph Theory 15 (1991), 99–107] lower bound on the independence number of aK-uniform hypergraph H. This bound has the form CK · ∑n i=1(di+1) −1/(K−1), where CK is a constant depending only on K, and d1, . . . , dn are the degrees of the vertices in H. We improve on the best known bounds for CK : in particular, we prove that C3 ≥ √π/2 and that CK ...
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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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For a positive integer q, a k-uniform hypergraph X = (V,E) is q-complementary if there exists a permutation θ on V such that the sets E,E, E 2 , . . . , E q−1 partition the set of k-subsets of V . The permutation θ is called a q-antimorphism of X. The well studied self-complementary uniform hypergraphs are 2-complementary. For an integer n and a prime p, let n(p) = max{i : p i divides n}. In th...
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We present a lower bound on the independence number of arbitrary hypergraphs in terms of the degree vectors. The degree vector of a vertex v is given by d(v) = (d 1 (v); d 2 (v); : : :) where d m (v) is the number of edges of size m containing v. We deene a function f with the property that any hypergraph H = (V; E) satisses (H) P v2V f(d(v)). This lower bound is sharp when H is a matching, and...
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Let K (3) 4 denote the complete 3-uniform hypergraph on 4 vertices. Ajtai, Erdős, Komlós, and Szemerédi (1981) asked if there is a function ω(d) → ∞ such that every 3-uniform, K (3) 4 -free hypergraph H with N vertices and average degree d has independence number at least N d1/2 ω(d). We answer this question by constructing a 3-uniform, K (3) 4 -free hypergraph with independence number at most ...
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ژورنال
عنوان ژورنال: Acta Universitatis Sapientiae, Informatica
سال: 2014
ISSN: 2066-7760
DOI: 10.2478/ausi-2014-0022