Infinite Matroidal Version of Hall's Matching Theorem | Zendy

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Infinite Matroidal Version of Hall's Matching Theorem

Author(s) -

Wojciechowski Jerzy

Publication year - 2005

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610705006320

Subject(s) - finitary , matroid , bipartite graph , combinatorics , mathematics , matching (statistics) , graphic matroid , discrete mathematics , rank (graph theory) , countable set , graph , statistics

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 ( 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. 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 ( M, W ) of finitary matroids, where the matroid M is SCF.

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