The fundamental cutset theorem is a result in graph theory and network analysis that states that in a connected graph, the minimum number of edges that must be removed to disconnect the graph is equal to the number of cutvertices in the graph. A cutvertex (also known as an articulation point) is a vertex whose removal increases the number of connected components in the graph.

A cutset is a subset of edges in a graph that, if removed, disconnects the graph. A cutset tree is a treelike representation of a graph that highlights the cutsets and cutvertices of the graph.

The fundamental cutset theorem and the concept of cutset trees are useful in network design and analysis, as they help identify the critical points in a network and the minimum number of components that must be protected in order to maintain network connectivity. They have applications in various fields, including electrical engineering, computer networks, and transportation planning.
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