The Matroid Ramsey Number n(6,6)
Joseph E. Bonin, Jennifer McNulty, Talmage James Reid · Combinatorics Probability Computing · 1999
A tight upper bound on the number of elements in a connected matroid with fixed rank and largest cocircuit size is given. This upper bound is used to show that a connected matroid with at least thirteen elements contains either a circuit or a cocircuit with at least six elements. In the language of matroid Ramsey numbers, n(6, 6) = 13: this is the largest currently known matroid Ramsey number.