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A simple binary matroid, viewed as a restriction of a finite binaryprojective geometry $PG(n-1,2)$, is $I_{1,t}$-free if for any rank-$t$ flat of$PG(n-1,2)$, its intersection with the matroid is not a one-element set. Inthis paper, we show that the simple $I_{1,t}$-free and triangle-free binarymatroids have bounded critical number for any $t \geq 1$.

The critical number of $I_{1,t}$-free triangle-free binary matroids