Skip to main content

Lectures on the marriage theorem of aharoni, nash-williams and shelah

  • Conference paper
  • First Online:
Graph Theory Singapore 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1073))

  • 520 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Aharoni, On the equivalence of two conditions for the existence of transversals, J. Comb. Theory, Ser. A. (to appear).

    Google Scholar 

  2. R. Aharoni, König's duality theorem for infinite bipartite graphs (to appear).

    Google Scholar 

  3. R. Aharoni, C. St. J. A. Nash-Williams & S. Shelah, A general criterion for the existence of transversals, Proc. Lond. Math. Soc., (3) 47 (1983), 43–68.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. M. Damerell & E. C. Milner, Necessary & sufficient conditions for transversals of countable set systems, J. Comb. Theory, Ser. A. 17 (1974), 350–379.

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Fodor, Eine Bemerkung zur Theorie der Regressiven Functionen, Acta Sci Math. (Szeged) 17 (1956), 139–142.

    MathSciNet  MATH  Google Scholar 

  6. J. Folkman, Transversals of infinite families with only finitely many infinite members, J. Comb. Theory, 9 (1970), 200–220.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Hall, Jr., Distinct representatives of subsets, Bull. Am. Math. Soc. 54 (1948), 922–926.

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Hall, On representatives of subsets, J. Lond. Math. Soc. 10 (1935), 26–30.

    MATH  Google Scholar 

  9. W. Hodges, In singular cardinalities, locally free algebras are free, Algebra Univers., 12 (1981), 205–220.

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Kőnig, Graphok es Matrixok, Mat. Fiz. Lapok. 38 (1932), 116–119. (Hungarian with German summary)

    Google Scholar 

  11. C. St. J. A. Nash-Williams, Another criterion for marriages in denumerable societies, Ann. Discrete Math. 3 (1978), 165–179.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. P. Podewski & K. Steffens, Injective choice functions for countable families, J. Comb. Theory, Ser. B. 21 (1976), 40–46.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. P. Podewski & K. Steffens, Maximal representable subfamilies, Bull. Lond. Math. Soc., 8 (1976), 186–189.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Rado, Note on the transfinite case of Hall's theorem on representatives, J. Lond. Math. Soc. 42 (1967), 321–324.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Shelah, Notes on partition Calculus, in Infinite & Finite Sets (Ed. A. Hajnal, R. Rado & V. Sos), Colloq. Math. Soc. Janos Bolyai, (1973), 1257–1276.

    Google Scholar 

  16. S. Shelah, A Compactness thoerem for singular cardinals, free algebras, Whitehead problem and transversals, Isr. J. Math. 21 (1975), 319–349.

    Article  MATH  Google Scholar 

  17. K. Steffens, Injective choice functions, J. Comb. Theory 17 (1974), 138–144.

    Article  MathSciNet  MATH  Google Scholar 

  18. D. R. Woodall, Two results on infinite transversals, Combinatorics, Inst. Math. Applications (1972), 341–350.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Khee Meng Koh Hian Poh Yap

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Milner, E.C. (1984). Lectures on the marriage theorem of aharoni, nash-williams and shelah. In: Koh, K.M., Yap, H.P. (eds) Graph Theory Singapore 1983. Lecture Notes in Mathematics, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073105

Download citation

  • DOI: https://doi.org/10.1007/BFb0073105

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13368-1

  • Online ISBN: 978-3-540-38924-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics