Abstract
Hartvigsen and Zemel have obtained a characterization of those graphs which have every circuit basis fundamental. We consider the corresponding problem for binary matroids. We show that, in general, the class of binary matroids for which every circuit basis is fundamental is not closed under the taking of minors. However, this class is closed under the taking of series-minors. We also describe some general properties of this class of matroids. We end by extending Hartvigsen and Zemel's result to the class of regular matroids, thus obtaining a set of excluded minors which are graphic for this class. © 1996 John Wiley & Sons, Inc.
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