Cross-intersecting pairs of hypergraphs

Aharoni, Ron; Howard, David M.

doi:10.1016/j.jcta.2016.12.002

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…Blocking sets and the blockers of set families (families are often regarded as the hyperedge families of hypergraphs) are discussed, e.g., in the monographs [11,22,29,31,32,43,46,48,50,51,53,54,56,67,70,72,73,78,79,81] and in the works [3,4,5,6,7,9,10,12,13,16,17,20,21,23,24,25,26,27,28,30,33,34,38,39,40,41,42,44,45,47,52,…”

Section: Blockingmentioning

confidence: 99%

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. V

Matveev

2021

Preprint

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We consider decompositions of topes of the oriented matroid realizable as the arrangement of coordinate hyperplanes in R 2 t , with respect to a distinguished symmetric 2 • 2 t -cycle in its hypercube graph of topes H(2 t , 2). We seek interpretations of such decompositions in the context of subset families on the ground set Et := {1, . . . , t} and of the families of their blocking sets, in the context of clutters on Et and of their blockers. Contents 1. Introduction Decomposing 2. Topes, their relabeled opposites, and decompositions Blocking 3. Increasing families of blocking sets, and blockers: Set covering problems 4. Families of subsets of the ground set E t : Characteristic vectors and characteristic topes 5. Increasing families of blocking sets, and blockers: Characteristic vectors and characteristic topes 5.1. A clutter {{a}} 5.1.1. The principal increasing family of blocking sets B({{a}}) = {{a}} 5.1.2. The blocker B({{a}}) = {{a}} 5.1.3. More on the principal increasing family B({{a}}) = {{a}} 5.2. A clutter {A} 5.2.1. The increasing family of blocking sets B({A}) = {{a} : a ∈ A} 5.2.2. The blocker B({A}) = {{a} : a ∈ A} 5.2.3. More on the increasing families {A} and B({A}) 5.3. A clutter A := {A 1 , . . . , A α } 5.3.1. The increasing family of blocking sets B(A) 5.3.2. The blocker B(A) 5.3.3. More on the increasing families A and B(A)

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Section: Blockingmentioning

confidence: 99%

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. V

Matveev

2021

Preprint

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On Rainbow Matchings for Hypergraphs

Lu¹,

Yu²

2018

SIAM J. Discrete Math.

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For any posotive integer m, let [m] := {1, . . . , m}. Let n, k, t be positive integers. Aharoni and Howard conjectured that if, forWe show that this conjecture holds when n ≥ 3(k − 1)(t − 1).Let n, t, k 1 ≥ k 2 ≥ . . . ≥ k t be positive integers. Huang, Loh and Sudakov asked for the maximum Π t i=1 |R i | over all R = {R 1 , . . . , R t } such that each R i is a collection of k i -subsets of [n] for which there does not exist a collection M of subsets of [n] such that |M | = t and |M ∩ R i | = 1 for i ∈ [t] We show that for sufficiently large n with

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Cross-intersecting pairs of hypergraphs

Cited by 2 publications

References 15 publications

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. V

Pattern Recognition on Oriented Matroids: Symmetric Cycles in the Hypercube Graphs. V

On Rainbow Matchings for Hypergraphs

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