Binary matroids with no \(PG(3,2)\)-minor. (English) Zbl 1160.05012
Summary: We show that a binary rank-\(r\) matroid with more than \(15r(r+1)/4\) points contains a minor isomorphic to the rank-4 binary projective geometry \(PG(3,2)\).
MSC:
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
| 05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
| 05C35 | Extremal problems in graph theory |
| 05D99 | Extremal combinatorics |
| 06C10 | Semimodular lattices, geometric lattices |
| 51M04 | Elementary problems in Euclidean geometries |
