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An effective version of Hall's theorem


Author: Henry A. Kierstead
Journal: Proc. Amer. Math. Soc. 88 (1983), 124-128
MSC: Primary 03D45; Secondary 05C70
DOI: https://doi.org/10.1090/S0002-9939-1983-0691291-0
MathSciNet review: 691291
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Abstract: Manaster and Rosenstein [1972] constructed a recursively bipartite highly recursive graph that satisfies Hall's condition for a bipartite graph to have a matching, but has no recursive matching. We discuss a natural extension of Hall's condition which assures that every such graph has a recursive matching.


References [Enhancements On Off] (What's this?)

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  • [P] Hall (1935) On representatives of subsets, J. London Math. Soc. 10, 26-30.
  • [M] Holz, K.-P. Podewski and K. Steffens (1979) Hall families and the marriage problem, J. Combinatorial Theory Ser. A 27, 161-180. MR 542526 (81e:04005)
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  • 1. -(1973) Effective matchmaking and $ k$-chromatic graphs, Proc. Amer. Math. Soc. 39, 371-378. MR 0340082 (49:4838)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0691291-0
Article copyright: © Copyright 1983 American Mathematical Society

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