I'm looking for a textbook reference of the cut property of minimum spanning trees analogous to that in the Wikipedia page, namely:
Cut property. For any cut $C$ of a graph, if the weight of an edge $e$ in the cut-set of $C$ is strictly smaller than the weights of all other edges of the cut-set of $C$, then this edge belongs to all minimum spanning trees of the graph.
Before posting this question, I've searched in several textbooks of graph theory/computer science/discrete mathematics. However, I've only found a "restricted" version of this property, wherein it is assumed that the underlying graph has different edge weights. Instead I'm interested in an explicit reference for the "general" version of the cut property (as reported above).
Any help is very welcome. Thank you.
https://people.eecs.berkeley.edu/~vazirani/s99cs170/notes/lec14.ps doesn't assume unequal edge weights.
Most text books avoid dealing with equal edge weights, as it is really inconsequential -- any algorithm to find an MST that works for unequal edge weights can be made to work for equal edge weights by choosing an arbitrary secondary characteristic to order the equal edges (ex. order in which the edges are represented in computer memory)