Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-23T23:33:22.847Z Has data issue: false hasContentIssue false
  • English
  • Français

The Matroid Ramsey Number n(6,6)

Published online by Cambridge University Press:  01 May 1999

JOSEPH E. BONIN ,
JENNIFER McNULTY  and
TALMAGE JAMES REID
JOSEPH E. BONIN
Affiliation:
Department of Mathematics, The George Washington University, Washington, DC, 20052, USA (e-mail: jbonin@gwis2.circ.gwu.edu)
JENNIFER McNULTY
Affiliation:
Department of Mathematical Sciences, The University of Montana, Missoula, MT 59812, USA (e-mail: mcnulty@selway.umt.edu)
TALMAGE JAMES REID
Affiliation:
Department of Mathematics, The University of Mississippi, University, MS 38677, USA (e-mail: mmreid@hilbert.math.olemiss.edu)
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 8 , Issue 3 , May 1999 , pp. 229 - 235
Copyright
1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)