Abstract
In this paper we present a Berge-Tutte-type theorem for a matching problem in directed graphs. This extends the maximum matching problem in undirected graphs, the maximum even factor problem in weakly symmetric directed graphs proposed by W. H. Cunningham and J. F. Geelen in [6], and a packing problem for cycles and edges in undirected graphs. We show an Edmonds-Gallai-type structural description of a canonical set attaining the minimum in the formula. We also give a generalization of the matching matroid to this concept.
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Research supported by the Hungarian National Foundation for Scientific Research Grant, OTKA T037547 and by European MCRTN Adonet, Contract Grant No. 504438.
The author is supported by the Egerváry Research Group of the Hungarian Academy of Sciences.
The author is a member of the Egerváry Research Group (EGRES).
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Pap, G., Szegő, L. Matchings of cycles and paths in directed graphs. Combinatorica 27, 383–398 (2007). https://doi.org/10.1007/s00493-007-2131-x
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DOI: https://doi.org/10.1007/s00493-007-2131-x