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In this paper we present a min-max theorem for a factorization problem in directed graphs. This extends the Berge-Tutte formula on matchings as well as formulas for the maximum even factor in weakly symmetric directed graphs and a factorization problem in undirected graphs. We also prove an extension to the structural theorem of Gallai and Edmonds about a canonical set attaining minimum in the formula. The matching matroid can be generalized to this context: we get a matroidal description of the coverable node sets.
Bibtex entry:
| AUTHOR | = | {Pap, Gyula and Szeg{\H o}, L{\'a}szl{\'o}}, |
| TITLE | = | {On factorizations of directed graphs by cycles}, |
| NOTE | = | {{\tt egres.elte.hu}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2004}, |
| NUMBER | = | {TR-2004-01} |