Graphs and Combinatorics

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

Finite union theorem with restrictions

  • Jaroslav Nešetřil
  • Vojtěch Rödl


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}.



Pairwise Disjoint Union Theorem Finite Union Arbitrary Partition Disjoint Element 
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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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