Typical subgraphs of 3- and 4-connected graphs
Journal of Combinatorial Theory Series B
Unavoidable minors of large 3-connected binary matroids
Journal of Combinatorial Theory Series B
European Journal of Combinatorics
The Matroid Ramsey Number n(6,6)
Combinatorics, Probability and Computing
An Upper Bound on the Number of Edges of a 2-Connected Graph
Combinatorics, Probability and Computing
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It has been conjectured that a connected matroid with largest circuit size c ≥ 2 and largest cocircuit size c* ≥ 2 has at most ½cc* elements. Pou-Lin Wu has shown that this conjecture holds for graphic matroids. We prove two special cases of the conjecture, not restricted to graphic matroids, thereby providing the first nontrivial evidence that the conjecture is true for non-graphic matroids. Specifically, we prove the special case of the conjecture in which c = 4 or c* = 4. We also prove the special case for binary matroids with c = 5 or c* = 5.