Partitions of a set V form a t-cover if each t-element subset is covered by some block of some partitions. The rank of a t-cover is the size of the largest block appearing. What is the minimum rank of a t-cover of an n-element set, consisting of r partitions? The main result says that it is at least n/q, where q is the smallest integer satisfying r ⩽ qt−1 + qt−2 + ⋯ + q + 1
AbstractAnswering a 25-year-old problem of Erdös and Gallai, we prove that if a set system H of rank...
AbstractConsider a hypergraph of rank r>2 with m edges, independence number α and edge cover number ...
Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. Wh...
Partitions of a set V form a t-cover if each t-element subset is covered by some block of some parti...
AbstractA set T is said to cover a set system J if T meets all members of J. We raise the following ...
AbstractLetDbe a finite family ofk-subsets (called blocks) of av-setX(v). ThenDis a (v, k, t) coveri...
AbstractDefine λ(n) to be the largest integer such that for each set A of size n and cover J of A, t...
A family of sets S = (S$ sb1$,S$ sb2$,...,S$ sb{m}$) is a k-fold cover for set T if each element of ...
Define [lambda](n) to be the largest integer such that for each set A of size n and cover J of A, th...
AbstractLet T(r, n) denote the maximum number of subsets of an n-set satisfying the condition in the...
AbstractIn the power set lattice of a finite set with n elements, a collection C of r element subset...
AbstractLet X be a finite set of n-melements and suppose t ⩾ 0 is an integer. In 1975, P. Erdös aske...
AbstractA t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices ...
For a finite set X, we say that a set H ⊆ X crosses a partition P = (X1, . . . , Xk) of X if H inter...
AbstractNew upper bounds for C(v,k,t), the minimum number of k-subsets (blocks) out of a v-set such ...
AbstractAnswering a 25-year-old problem of Erdös and Gallai, we prove that if a set system H of rank...
AbstractConsider a hypergraph of rank r>2 with m edges, independence number α and edge cover number ...
Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. Wh...
Partitions of a set V form a t-cover if each t-element subset is covered by some block of some parti...
AbstractA set T is said to cover a set system J if T meets all members of J. We raise the following ...
AbstractLetDbe a finite family ofk-subsets (called blocks) of av-setX(v). ThenDis a (v, k, t) coveri...
AbstractDefine λ(n) to be the largest integer such that for each set A of size n and cover J of A, t...
A family of sets S = (S$ sb1$,S$ sb2$,...,S$ sb{m}$) is a k-fold cover for set T if each element of ...
Define [lambda](n) to be the largest integer such that for each set A of size n and cover J of A, th...
AbstractLet T(r, n) denote the maximum number of subsets of an n-set satisfying the condition in the...
AbstractIn the power set lattice of a finite set with n elements, a collection C of r element subset...
AbstractLet X be a finite set of n-melements and suppose t ⩾ 0 is an integer. In 1975, P. Erdös aske...
AbstractA t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices ...
For a finite set X, we say that a set H ⊆ X crosses a partition P = (X1, . . . , Xk) of X if H inter...
AbstractNew upper bounds for C(v,k,t), the minimum number of k-subsets (blocks) out of a v-set such ...
AbstractAnswering a 25-year-old problem of Erdös and Gallai, we prove that if a set system H of rank...
AbstractConsider a hypergraph of rank r>2 with m edges, independence number α and edge cover number ...
Computing a minimum vertex cover in graphs and hypergraphs is a well-studied optimizaton problem. Wh...
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