Let $M = (E, mathcal{F})$ be a matroid on a set $E$ and $B$ one of its bases. A closed set $heta subseteq E$ is saturated with respect to $B$ when $|heta cap B | leq r(heta)$, where $r(heta)$ is the rank of $heta$. The collection of subsets $I$ of $E$ such that $| I cap heta| leq r(heta)$ for every closed saturated set $heta$ turns out to be the family of independent sets of a new matroid on $E$, called base-matroid and denoted by $M_B$. In this paper we prove that a graphic matroid $M$, isomorphic to a cycle matroid $M(G)$, is isomorphic to $M_B$, for every base $B$ of $M$, if and only if $M$ is direct sum of uniform graphic matroids or, in equivalent way, if and only if $G$ is disjoint union of cacti. Moreover we characterize simple binary matroids $M$ isomorphic to $M_B$, with respect to an assigned base $B$.
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机译：让$ m =（e， mathcal {f}）$是一个MATROID，在套装$ E $和$ B $之一。封闭式$ Theta subseteq e $饱和在$ b $ ware $ | theta cap b | leq r（ theta）$，其中$ r（ theta）$是$ theta $的排名。亚特的集合$ i $ e $，以至于$ |我 cap theta | Leq R（ Theta）$的每一个封闭的饱和设置$ theta $ of to the $ e $的独立套装系列，称为基础matroid，并表示为$ m_b $表示。在本文中，我们证明了一个图形Matroid $ M $，Irsomorphic到循环Matroid $ M（g）$，是每一份为$ m_b $，因为只有$ m $的每一个基本$ b $，如果才有m $是均匀图形matroid的直接和，或者以等效的方式，如果才能才有v $ of $ cacti联合。此外，我们将简单的二进制Matroids为$ M $ Insomorphic鉴定为$ M_B $，以及指定的基准$ B $。
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