Abstract
A simple binary matroid is called claw-free if none of its rank-3 flats are independent sets. These objects can be equivalently defined as the sets E of points in PG(n−1,2) for which E∩P is not a basis of P for any plane P, or as the subsets X of F2n containing no linearly independent triple x,y,z for which x+y,y+z,x+z,x+y+z∉X.We prove a decomposition theorem that exactly determines the structure of all claw-free matroids. The theorem states that claw-free matroids either belong to one of three particular basic classes of claw-free matroids, or can be constructed from these basic classes using a certain ‘join’ operation.
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