Extremal critically connected matroids
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A connected matroid M is called a critically connected matroid if the deletion of any one element from M results in a disconnected matroid. We show that a critically connected matroid of rank n, n>=3, can have at most 2n-2 elements. We also show that a critically connected matroid of rank n on 2n-2 elements is isomorphic to the forest matroid of K"2, n-2.
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