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To a student in linear graph theory, many concepts which later become almost second nature often need at first step-by-step, concrete demonstrations. For example, cut sets and cut vertices become increasingly meaningful if the student is given a procedure whereby he, by himself, can correctly and confidently identify all cut sets and cut vertices in any given graph no matter how complex. For this purpose, an earlier definition of ambits is extended to provide the basis for a combinatorial method for finding all cut sets and cut vertices of a connected graph. As by-products, interesting properties of ambits are disclosed.