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Counting and constructing minimal spanning trees. (English) Zbl 0886.05049
The paper presents an algorithm for constructing minimal spanning trees in a network. It is based on the known result that any two minimal spanning trees in a network have the same number of edges of weight $$k$$ for each $$k$$, suggesting the possibility of partitioning the minimal tree construction process. An algorithm to this effect is outlined as well as a formula for the number of minimal spanning trees.
##### MSC:
 05C05 Trees 05C30 Enumeration in graph theory 94C15 Applications of graph theory to circuits and networks 94C05 Analytic circuit theory
##### Keywords:
algorithm; minimal spanning trees; network