The Matroid Ramsey Number n(6,6)

Authors:
Joseph E. Bonin;Jennifer McNulty;Talmage James Reid
Affiliations:
Department of Mathematics, The George Washington University, Washington, DC, 20052, USA (e-mail: jbonin@gwis2.circ.gwu.edu);Department of Mathematical Sciences, The University of Montana, Missoula, MT 59812, USA (e-mail: mcnulty@selway.umt.edu);Department of Mathematics, The University of Mississippi, University, MS 38677, USA (e-mail: mmreid@hilbert.math.olemiss.edu)
Venue:
Combinatorics, Probability and Computing
Year:
1999

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Abstract

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.