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21st Cumberland Conference on Graph Theory, Combinatorics, and Computing ---In Honor of Mike Plummer's 70th Birthday
May 15-17, 2008
Vanderbilt University
Nashville, TN, USA

Organizers
Mark Ellingham and Gexin Yu

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Infinite matroids and Hall's matching theorem
by
Jerzy Wojciechowski
West Virginia University

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 generalized the notion of matchability to a pair of possibly infinite matroids on the same set and gave a condition that is sufficient for the matchability of a given pair ( M, W) of finitary matroids, where the matroid M is SCF - a sum of countably many matroids of finite rank. The condition of Aharoni and Ziv is not necessary for matchability. We will discuss another condition for matchability, that uses transfinite sequences and is defined in analogy to Nash-Williams condition for matchability of countable bipartite graphs.

Date received: May 1, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-64.