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We address here spanning tree problems on a graph with binary edge weights.For a general weighted graph the minimum spanning tree is solved insuper-linear running time, even when the edges of the graph are pre-sorted. Arelated problem, of finding a spanning tree with a pre-specified sum ofweights, is NP-hard. In contrast, for a graph with binary weights associatedwith the edges, it is shown that the minimum spanning tree and finding aspanning tree with a given total sum, are solvable in linear time with simplealgorithms.

Binary weights spanning trees and the $k$-red spanning tree problem in linear time