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Graphs and Combinatorics

, Volume 2, Issue 1, pp 357–361 | Cite as

Finite union theorem with restrictions

  • Jaroslav Nešetřil
  • Vojtěch Rödl
Article

Abstract

The aim of this paper is to prove the following extension of the Folkman-Rado-Sanders Finite Union Theorem: For every positive integersr andk there exists a familyL of sets having the following properties:
  1. i)

    ifS1,S2, ...,Sk + 1 are distinct pariwise disjoint elements ofL then there exists nonemptyI ⊂ {1, 2, ...,k + 1} with ∪ i∈I S i L

     
  2. ii)

    ifL =L1 ⋃...⋃L r is an arbitrary partition then there existsj ≤ r and pairwise disjoint setsS1,S2, ...,S k L j , such thatLi∈IS i L j for every nonemptyI ⊂ {1, 2, ...,k}.

     

Keywords

Pairwise Disjoint Union Theorem Finite Union Arbitrary Partition Disjoint Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Jaroslav Nešetřil
    • 1
  • Vojtěch Rödl
    • 2
  1. 1.Department of MathematicsCharles UniversityPraha 1Czechoslovakia
  2. 2.Department of MathematicsFJFI, ČVUTPraha 1Czechoslovakia

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