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Maximum-Sized Matroids with No Minors Isomorphic to U2,5, F7, F−7 or P7

Published online by Cambridge University Press:  10 December 2001

STEFAN T. MECAY
STEFAN T. MECAY
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203, USA Department of Mathematics, Schreiner University, Kerrville, TX 78028, USA; (e-mail: stefan@ktc.com)
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Abstract

Let [Mscr ] be the class of simple matroids which do not contain the 5-point line U2,5, the Fano plane F7, the non-Fano plane F−7, or the matroid P7 as minors. Let h(n) be the maximum number of points in a rank-n matroid in [Mscr ]. We show that h(2) = 4, h(3) = 7, and h(n) = (n+12) for n [ges ] 4, and we also find all the maximum-sized matroids for each rank.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 10 , Issue 6 , November 2001 , pp. 531 - 542
Copyright
2001 Cambridge University Press

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