Abstract
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 - 15 k 9 , 5 r * ( M ) + 30 - 10 k 7 elements covered by triangles. For each k, an infinite family of matroids that attain this bound is constructed.
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