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Define fragment of a MST T to be a sub-tree of T, that is, a connected set of nodes and edges of T. There are two properties of MSTs:
# Given a fragment of a MST T, let e be a minimum-weight outgoing edge of the fragment. Then joining e and its adjacent non-fragment node to the fragment yields another fragment of
# If all the edges of a connected graph have different weights, then the MST of the graph is unique.<ref name="GHS" />
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