Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Aharoni, On the equivalence of two conditions for the existence of transversals, J. Comb. Theory, Ser. A. (to appear).
R. Aharoni, König's duality theorem for infinite bipartite graphs (to appear).
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.
R. M. Damerell & E. C. Milner, Necessary & sufficient conditions for transversals of countable set systems, J. Comb. Theory, Ser. A. 17 (1974), 350–379.
G. Fodor, Eine Bemerkung zur Theorie der Regressiven Functionen, Acta Sci Math. (Szeged) 17 (1956), 139–142.
J. Folkman, Transversals of infinite families with only finitely many infinite members, J. Comb. Theory, 9 (1970), 200–220.
M. Hall, Jr., Distinct representatives of subsets, Bull. Am. Math. Soc. 54 (1948), 922–926.
P. Hall, On representatives of subsets, J. Lond. Math. Soc. 10 (1935), 26–30.
W. Hodges, In singular cardinalities, locally free algebras are free, Algebra Univers., 12 (1981), 205–220.
D. Kőnig, Graphok es Matrixok, Mat. Fiz. Lapok. 38 (1932), 116–119. (Hungarian with German summary)
C. St. J. A. Nash-Williams, Another criterion for marriages in denumerable societies, Ann. Discrete Math. 3 (1978), 165–179.
K. P. Podewski & K. Steffens, Injective choice functions for countable families, J. Comb. Theory, Ser. B. 21 (1976), 40–46.
D. P. Podewski & K. Steffens, Maximal representable subfamilies, Bull. Lond. Math. Soc., 8 (1976), 186–189.
R. Rado, Note on the transfinite case of Hall's theorem on representatives, J. Lond. Math. Soc. 42 (1967), 321–324.
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.
S. Shelah, A Compactness thoerem for singular cardinals, free algebras, Whitehead problem and transversals, Isr. J. Math. 21 (1975), 319–349.
K. Steffens, Injective choice functions, J. Comb. Theory 17 (1974), 138–144.
D. R. Woodall, Two results on infinite transversals, Combinatorics, Inst. Math. Applications (1972), 341–350.
Author information
Authors and Affiliations
Editor information
Rights 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