نتایج جستجو برای: union closed sets conjecture
تعداد نتایج: 414131 فیلتر نتایج به سال:
Frankl’s union-closed sets conjecture states that in every finite unionclosed family of sets, not all empty, there is an element in the ground set contained in at least half of the sets. The conjecture has an equivalent formulation in terms of graphs: In every bipartite graph with least one edge, both colour classes contain a vertex belonging to at most half of the maximal stable sets. We prove...
Let [n]:={1,2,…,n} and let a k-set denote set of cardinality k. A family sets is union-closed (UC) if the union any two in also family. Frankl’s conjecture states that for nonempty UC F⊆2[n] such F≠{∅}, there exists an element i∈[n] contained at least half F, where 2[n] denotes power on [n]. The 3-sets Morris smallest number distinct (whose n-set) ensure satisfied (in contains them ⌊n/2⌋+1 all ...
Let F be a union-closed family of subsets of an m-element set A. Let n = |F| ≥ 2. For b ∈ A let w(b) denote the number of sets in F containing b minus the number of sets in F not containing b. Frankl’s conjecture from 1979, also known as the union-closed sets conjecture, states that there exists an element b ∈ A with w(b) ≥ 0. The present paper deals with the average of the w(b), computed over ...
let g=(v,e) be a graph with vertex set v and edge set e.for two vertices u,v of g ,the closed interval i[u,v] ,consists of u,v and all vertices lying in some u-v geodesic in g.if s is a set of vertices of g then i[s]is the union of all sets i[u,v]for u,v ? s. if i[s]=v(g) , then s is a geodetic set for g.the geodetic number g(g) is the minimum cardinality of geodetic set.the maximum cardinalit...
We shall show that the union-closed families conjecture holds for a random union-closed family with high probability. This strengthens a recent result of Bruhn and Schaudt.
in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.
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