Abstract
Let G be a graph, possibly infinite. Three successively larger sets of matchings in G are defined, the maximum, locally maximum, and quasi-locally maximum matchings. If G is finite the matchings of each type are maximum matchings in G. The maximum and locally maximum matchings are characterized in terms of alternating paths. Not every graph has a maximum matching, but Rado's selection theorem is used to show that every graph has a quasi-locally maximum matching. If G is locally finite, then G has a maximum matching, and every quasi-locally maximum matching in G is locally maximum.
Research supported by University of Kansas General Research allocation 3239-5038.
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References
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© 1978 Springer-Verlag Berlin Heidelberg
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McCarthy, P.J. (1978). Matchings in graphs III: Infinite graphs. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070395
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DOI: https://doi.org/10.1007/BFb0070395
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