The complexity of Bottleneck Labeled Graph Problems

In the present paper, we study 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 color.