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null (Ed.)The existence of a rainbow matching given a minimum color degree, proper coloring, or triangle-free host graph has been studied extensively. This paper generalizes these problems to edge colored graphs with given total color degree. In particular, we find that if a graph $$G$$ has total color degree $2mn$ and satisfies some other properties, then $$G$$ contains a matching of size $$m$$. These other properties include $$G$$ being triangle-free, $$C_4$$-free, properly colored, or large enough.more » « less
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