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INFINITE MATROIDAL VERSION OF HALL'S MATCHING THEOREM

Published online by Cambridge University Press:  24 May 2005

JERZY WOJCIECHOWSKI
JERZY WOJCIECHOWSKI
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, [email protected]
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Abstract

Hall's theorem for bipartite graphs gives a necessary and sufficient condition for the existence of a matching in a given bipartite graph. Aharoni and Ziv have generalized the notion of matchability to a pair of possibly infinite matroids on the same set and given a condition that is sufficient for the matchability of a given pair $(\mathcal{M},\mathcal{W})$ of finitary matroids, where the matroid $\mathcal{M}$ is SCF (a sum of countably many matroids of finite rank). The condition of Aharoni and Ziv is not necessary for matchability. The paper gives a condition that is necessary for the existence of a matching for any pair of matroids (not necessarily finitary) and is sufficient for any pair $(\mathcal{M},\mathcal{W})$ of finitary matroids, where the matroid $\mathcal{M}$ is SCF.

Keywords

05B3505D15
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 563 - 578
Copyright
The London Mathematical Society 2005

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