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Some Small Circuit-Cocircuit Ramsey Numbers for Matroids

Published online by Cambridge University Press:  12 September 2008

Fair Barbour Hurst  and
Talmage James Reid
Fair Barbour Hurst
Affiliation:
Department of Mathematics, The University of Mississippi, University, MS 38677, U.S.A.
Talmage James Reid
Affiliation:
Department of Mathematics, The University of Mississippi, University, MS 38677, U.S.A.
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Abstract

Ramsey numbers for matroids, which mimic properties of Ramsey numbers for graphs, have been denned as follows. Let k and l be positive integers. Then n(k, l) is the least positive integer n such that every connected matroid with n elements contains either a circuit with at least k elements or a cocircuit with at least l elements. We determine the largest known value of these numbers in the sense of maximizing both k and l. We also find extremal matroids with small circuits and cocircuits. Results on matroid connectivity, geometry, and extremal matroid theory are used here.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 1 , March 1995 , pp. 67 - 80
Copyright
Copyright © Cambridge University Press 1995

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