We present hardness results, approximation heuristics, and exact algorithms for bottleneck labeled optimization problems arising in the context of graph theory. This long-established model partitions the set of edges into classes, each of which is identified by a unique color. The generic objective is to construct a subgraph of prescribed structure (such as that of being an s-t path, a spanning tree, or a perfect matching) while trying to avoid over-picking or under-picking edges from any given

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... color. ⋆ Due to space limitations, some proofs were omitted from this extended abstract. We refer the reader to the full version of this paper (currently available online at http://www.lamsade.dauphine.fr/∼monnot), in which all missing details are provided.