An element e of a 3-connected matroid M is said to be superfluous provided M/e is 3-connected. In this paper, we show that a 3-connected matroid M with exactly k superfluous elements has at least max {(5|E(M)|+30-15k)/9, (5r~*(M)+30-10k)/7} elements covered by triangles. For each k, an infinite family of matroids that attain this bound is constructed.
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