Linearly-dense classes of matroids with bounded branch-width
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Date
2017-09-27
Authors
Hill, Owen
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Let $M$ be a non-empty minor-closed class of matroids with bounded
branch-width that does not contain arbitrarily large
simple rank-$2$ matroids. For each non-negative integer
$n$ we denote by $ex(n)$ the size of the largest simple matroid
in $M$ that has rank at most $n$. We prove that there exist
a rational number $\Delta$ and a periodic sequence $(a_0,a_1,\ldots)$
of rational numbers such that $ex(n) = \Delta n+a_n$
for each sufficiently large integer $n$.